Time-metric equivalence and dimension change under time reparameterizations (2009)
Motter, Adilson E., Gelfert, Katrin
We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical...
On the distribution of periodic orbits (2009)
Gelfert, Katrin, Wolf, Christian
Let $f:M\to M$ be a $C^{1+\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\Lambda\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results...
Lyapunov spectrum for rational maps (2008)
Gelfert, Katrin, Przytycki, Feliks, Rams, Michal
We study the dimension spectrum of Lyapunov exponents for rational maps on the Riemann sphere.
Equality of pressures for diffeomorphisms preserving hyperbolic measures (2008)
For a diffeomorphism which preserves a hyperbolic measure the potential $\phi^u=-\log|{\rm Jac} df|_{E^u}|$ is studied. Various types of pressure of $\phi^u$ are introduced. It is shown that these...
Abstract. For nonconformal repellers satisfying a certain cone condition, we establish a version of multifractal analysis for the topological entropy of the level sets of the Lyapunov exponents. Due...
Holger Kantz, Wolfram Just, Nilüfer Baba, Katrin Gelfert, Anja Rieger
We show in detail how methods of time series analysis such as dimension and entropy estimates support the idea that fast low-dimensional chaos can be modeled properly by noise. Motivated by this...
The Lyapunov spectrum of some parabolic systems (2007)
We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given...
Topological pressure for one-dimensional holomorphic dynamical systems (2007)
Gelfert, Katrin, Wolf, Christian
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials h the topological pressure is entirely determined by the values of h on the...
Topological pressure via saddle points (2005)
Gelfert, Katrin, Wolf, Christian
Let $\Lambda$ be a compact locally maximal invariant set of a $C^2$-diffeomorphism $f:M\to M$ on a smooth Riemannian manifold $M$. In this paper we study the topological pressure $P_{\rm top}(\phi)$...
Elimination of Fast Chaotic Degrees of Freedom: On the accuracy of the Born approximation (2003)
Wolfram Just, Katrin Gelfert, Nilüfer Baba, Anja Riegert, Holger Kantz
We apply standard projection operator techniques known from nonequilibrium statistical mechanics to eliminate fast chaotic degrees of freedom in a low{dimensional dynamical system. Through the usual...
Hausdorff dimension estimates by use of a tubular Caratheodory structure (2000)
Katrin Gelfert, Gennady A. Leonov, Volker Reitmann
The paper is concerned with upper bounds for the Hausdorff dimension of flow invariant compact sets on Riemannian manifolds. The proof of the main theorem uses a special Caratheodory dimension...