Bernd O. Stratmann, Mariusz Urbański, Michel Zinsmeister
Abstract. In this paper we consider rational functions f: C → C with parabolic and critical points contained in their Julia sets J(f) such that n=1 |(f n) ′ (f(c)) | −1 < ∞ for each...
Variations of Hausdorff Dimension in the Exponential Family (2010)
Havard, Guillaume, Urbanski, Mariusz, Zinsmeister, Michel
In this paper we deal with the following family of exponential maps $(f_\lambda:z\mapsto \lambda(e^z-1))_{\lambda\in [1,+\infty)}$. Denoting $d(\lambda)$ the hyperbolic dimension of $f_\lambda$. It...
VARIATIONS OF HAUSDORFF DIMENSION IN THE EXPONENTIAL FAMILY (2009)
Guillaume Havard, Mariusz Urbański, Michel Zinsmeister
Abstract. In this paper we deal with the following family of exponential maps (fλ: z ↦ → λ(e z − 1))λ∈[1,+∞). Denoting d(λ) the hyperbolic dimension of fλ. It is proved in [Ur,Zd 1]...
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
On the time schedule of Brownian Flights (2009)
Batakis, Athanasios, Zinsmeister, Michel
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
Le problème de Helmholtz pour des obstacles peu réguliers (2009)
Erba, Carole, Weber, Régine, Zinsmeister, Michel
We show the existence of an infinite wake in the sense of Helmholtz for symmetric obstacles in the plane generated by a Lavrentiev curve with small constant.
Le problème de Helmholtz pour des obstacles peu réguliers (2009)
Erba, Carole, Weber, Régine, Zinsmeister, Michel
We show the existence of an infinite wake in the sense of Helmholtz for symmetric obstacles in the plane generated by a Lavrentiev curve with small constant.
Le problème de Helmholtz pour des obstacles peu réguliers (2009)
Erba, Carole, Weber, Régine, Zinsmeister, Michel
We show the existence of an infinite wake in the sense of Helmholtz for symmetric obstacles in the plane generated by a Lavrentiev curve with small constant.
Variations of Hausdorff Dimension in the Exponential Family (2008)
Havard, Guillaume, Urbanski, Mariusz, Zinsmeister, Michel
In this paper we deal with the following family of exponential maps $(f_\lambda:z\mapsto \lambda(e^z-1))_{\lambda\in [1,+\infty)}$. Denoting $d(\lambda)$ the hyperbolic dimension of $f_\lambda$. It...
Variations of Hausdorff Dimension in the Exponential Family (2008)
Havard, Guillaume, Urbanski, Mariusz, Zinsmeister, Michel
In this paper we deal with the following family of exponential maps $(f_\lambda:z\mapsto \lambda(e^z-1))_{\lambda\in [1,+\infty)}$. Denoting $d(\lambda)$ the hyperbolic dimension of $f_\lambda$. It...
Variations of Hausdorff Dimension in the Exponential Family (2008)
Havard, Guillaume, Urbanski, Mariusz, Zinsmeister, Michel
In this paper we deal with the following family of exponential maps $(f_\lambda:z\mapsto \lambda(e^z-1))_{\lambda\in [1,+\infty)}$. Denoting $d(\lambda)$ the hyperbolic dimension of $f_\lambda$. It...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase. (2007)
Mariusz Urbanski, Michel Zinsmeister
Let f 0 (z) = z 2 +1=4 and the set of phases such that the critical point 0 escapes in one step by the Lavaurs map g ; it is a topological strip in the cylinder of phases whose boundary consists of...
Geometry Of Hyperbolic Julia-Lavaurs Sets (2007)
Mariusz Urbanski, Michel Zinsmeister
. Let J be the Julia-Lavaurs set of a hyperbolic Lavaurs map g and let h be its Hausdor dimension. We show that the upper ball-(box) counting dimension and the Hausdor dimension of J are equal, that...
Bernd O. Stratmann, Mariusz Urba Nski, Michel Zinsmeister
Abstract. In this paper we consider rational functions f: CI! CI with parabolic and critical points contained in their Julia sets J(f) such that P 1
WELL-APPROXIMABLE POINTS FOR JULIA SETS WITH PARABOLIC AND CRITICAL POINTS (2007)
Bernd O. Stratmann, Mariusz Urba, Michel Zinsmeister
Abstract. In this paper we consider rational functions f: CI! CI with parabolic and critical points contained in their Julia sets J(f) such that lim n!1 j(f n
Mariusz Urbanski, Michel Zinsmeister
Continuity of Hausdor dimension of Julia-Lavaurs sets as a function of the phase.
GEOMETRY OF HYPERBOLIC JULIA-LAVAURS SETS MARIUSZ URBA (2007)
Abstract. Let J be the Julia-Lavaurs set of a hyperbolic Lavaurs map g and let h be its Hausdor dimension. We show that the upper ball-(box) counting dimension and the Hausdor dimension of J are...
Well-Approximable Points for Julia Sets with Parabolic and Critical Points (2007)
Bernd O. Stratmann, Mariusz Urbanski, Michel Zinsmeister
In this paper we consider rational functions f : C ! C with parabolic and critical points contained in their Julia sets J(f) such that < 1 for each critical point c 2 J(f ). We calculate the...
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\epsilon$ of K and start a Brownian motion (BM) from this point. We study the probability that...
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability...
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability...
On the product of functions in BMO and H$^\text{1}$ (2007)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability...
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability...
Batakis, Athanasios, Levitz, Pierre, Zinsmeister, Michel
Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, B.
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, B.
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, Bernard
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
On the Product of Functions in BMO and H1 (2006)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
La dualite H1-BMO n'est pas comme la dualite entre L^p et L^p' donnee par l'integrale du produit qui est integrable. Neammoins on peut donner un sens au produit d'une fonction de H1 et d'une fonction...
On the Product of Functions in BMO and H1 (2006)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
La dualite H1-BMO n'est pas comme la dualite entre L^p et L^p' donnee par l'integrale du produit qui est integrable. Neammoins on peut donner un sens au produit d'une fonction de H1 et d'une fonction...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, Bernard
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, Bernard
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
On the Product of Functions in BMO and H1 (2006)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
La dualite H1-BMO n'est pas comme la dualite entre L^p et L^p' donnee par l'integrale du produit qui est integrable. Neammoins on peut donner un sens au produit d'une fonction de H1 et d'une fonction...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, Bernard
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
On the Product of Functions in BMO and H1 (2006)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
La dualite H1-BMO n'est pas comme la dualite entre L^p et L^p' donnee par l'integrale du produit qui est integrable. Neammoins on peut donner un sens au produit d'une fonction de H1 et d'une fonction...
Brownian flights over a fractal nest and first-passage statistics on irregular surfaces (2006)
Levitz, P., Grebenkov, D.S., Zinsmeister, Michel, Kolwankar, K.M., Sapoval, Bernard
The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confining inter-...
On the Product of Functions in BMO and H1 (2006)
Bonami, Aline, Iwaniec, Tadeusz, Jones, Peter, Zinsmeister, Michel
La dualite H1-BMO n'est pas comme la dualite entre L^p et L^p' donnee par l'integrale du produit qui est integrable. Neammoins on peut donner un sens au produit d'une fonction de H1 et d'une fonction...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that the smallest...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that the smallest...
Variation of the conformal radius (2004)
Rhode, Steffen, Zinsmeister, Michel
We study the change of the conformal radius r(U) of a simply con- nected planar domain U versus the subdomain Uǫ consisting of the points of distance at least ǫ to ∂U. We show that the smallest...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are equal, that...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are equal, that...
Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let $ f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0} $ the set of phases $\overline{\sigma}$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma}$; it is a topological strip...
Geometry of hyperbolic Julia-Lavaurs sets (2001)
Urbanski, Mariusz, Zinsmeister, Michel
Let J_σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of Jσ are equal, that...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Havard, Guillaume, Zinsmeister, Michel
Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^2+c$. The function d restricted to [0,+X) is real analytic in $[0,\frac{1}{4})\cup (\frac{1}{4},+\infty)$...
Espaces de Hardy généralisés.
Th.3e cycle--Math. pures--Paris 11--Orsay, 1981. N°: 2952.