THERMODYNAMIC FORMALISM FOR RANDOM COUNTABLE MARKOV SHIFTS (2009)
Manfred Denker, Yuri Kifer, Manuel Stadlbauer
Dedicated to Yakov Pesin on the occasion of his sixtieth birthday. Abstract. We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the...
Pseudorandom Numbers for Conformal Measure (2009)
Denker, Manfred, Duan, Jinqiao, McCourt, Michael
We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential F. In...
zur Erlangung des Doktorgrades (2009)
Arnd Lauber, Koreferent Prof, Dr. Manfred Denker
Tag der mündlichen Prüfung: This thesis deals with Baker domains and approximation of Julia sets, so it belongs to the area of ”Holomorphic Dynamical Systems”. Dynamical systems belong to the...
zur Erlangung des Doktorgrades (2008)
Arnd Lauber, Koreferent Prof, Dr. Manfred Denker
Tag der mündlichen Prüfung: This thesis deals with Baker domains and approximation of Julia sets, so it belongs to the area of ”Holomorphic Dynamical Systems”. Dynamical systems belong to the...
zur Erlangung des Doktorgrades (2008)
Der Mathematisch–naturwissenschaftlichen Fakultäten, Referent Prof, Dr. Edgar Brunner, Koreferent Prof, Dr. Manfred Denker
vorgelegt von
A NOTE ON THE CONSTRUCTION OF NONSINGULAR GIBBS MEASURES (2007)
Manfred Denker, Michiko Yuri, Dedicated Prof, Anzelm Iwanik
Abstract. We give a sucient condition for the construction of Markov bred systems using countable Markov partitions with local bounded distortion. Let X be a compact metric space with metric d and T:...
Gibbs Measures For Fibred Systems (2007)
Manfred Denker, Mikhail Gordin
. We consider a topological dynamical system T : Y ! Y on a metric space Y which forms a fibre bundle over another dynamical system. If T is fibrewise expanding and exact along fibres and if '...
Thermodynamic Formalism, Large Deviation, and Multifractals (2007)
Manfred Denker, Marc Kesseböhmer
The spectral gap of the transfer operator for an expanding dynamical systems relates large deviation and local limit theorems. We discuss this phenomenon and state a local large deviation theorem in...
The Central Limit Theorem For Random Perturbations Of Rotations (2007)
Manfred Denker, Mikhail Gordin
. We prove a functional central limit theorem for stationary random sequences given by the transformations T ffl;! (x; y) = (2x; y + ! + fflx) mod 1 on the two-dimensional torus. This result is based...
The Poincaré Series Of C\Z (2007)
. We show that the Poincar'e series of the Fuchsian group of deck transformations of C nZdiverges logarithmically. This is because C nZis a Z-cover of the three horned sphere, whence its...
. We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions. x1 Introduction It is well known that a random variable X belongs to the domain of...
We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions.
In November 1996, the German national science foundation DFG (2007)
Sponsored Workshop, Manfred Denker, Stefan-m. Heinemann, Bernd Stratmann
multifractal intersection schemes, work in progress, 1997 [31] L. Olsen, Multifractal geometry. A survey, work in progress, 1997 [32] N. Patzschke, Self-conformal multifractals, preprint, 1996 [33]...
PDMI PREPRINT--- 19/2002 A Poisson limit theorem for toral automorphisms (2007)
Manfred Denker, Mikhail Gordin, Anastasya Sharova
We introduce a new method of proving Poisson limit laws in the theory of dynamical systems, which is based on the Chen-Stein method ([7, 20]) combined with the analysis of the homoclinic Laplace...
Manfred Denker, Mikhail Gordin
In [4] we investigated the existence and uniqueness of a system of conditional measures for fibred systems which plays a similar role as conformal measures for non-fibred onedimensional dynamical...
On the Relative Variational Principle for Fibre Expanding Maps (2000)
Manfred Denker, Mikhail Gordin, Stefan-m. Heinemann
A bred dynamical system whose bre maps are uniformly expanding and exact, possesses, for every Holder continuous potential, a Gibbs family of conditional measures on its bres [DG2]. Such a family is...
Reflections on Harmonic Analysis of the Sierpinski Gasket (2000)
: Based on the geometric structure of the Sierpinski gasket, Kigami[K1, K2] established the harmonic analysis for the gasket analytically. On the other hand Denker and Sato[DS1] proved that the...
Sato: Sierpi`nski gasket as a Martin boundary I: Martin kernel. To appear: Potential Analysis (1999)
Abstract: It is shown in [DS] that the Sierpi'nski gasket S ae IR N can be represented as the Martin boundary of a certain Markov chain and hence carries a canonical metric ae M induced by the...
Group Extensions Of Gibbs-Markov Maps (1999)
. Let be an aperiodic cocycles with values in a locally compact abelian second countable group G dened on an exact Gibbs-Markov map T : X ! X. We show that the group extension T (x; g) = (T (x); g +...
Sierpinski Gasket As A Martin Boundary (1999)
. We show that a Sierpi'nski gasket in N dimension is homeomorphic to the minimal Martin boundary of some Markov chain which is not irreducible and does not have the bounded range structure. x1...
A Poisson Formula For Harmonic Functions On The Sierpinski Gasket (1999)
We show a Poisson formula for bounded harmonic functions \Phi on the Sierpi'nski gasket S. We construct a boundary (\Sigma ? ; ? ), a continuous action of a semigroup W on \Sigma ? and a map...
Sierpinski Gasket as a Martin Boundary II (The Intrinsic Metric) (1999)
: It is shown in [DS] that the Sierpi'nski gasket S ae IR N can be represented as the Martin boundary of a certain Markov chain and hence carries a canonical metric ae M induced by the embedding...
Exact Group Extensions Of Markov Maps. (1999)
. We give conditions for the exactness of R d -extensions of Markov maps. x0 Introduction A nonsingular transformation (X; B; m;T ) of a standard probability space is called a Markov map if there is...
Conservativity of random Markov fibred systems (1999)
Manfred Denker, Yuri Kifer, Manuel Stadlbauer
Abstract. In this paper we extend results concerning conservativity and the existence of-finite measures to random transformations which admit a countable relative Markov partition. In here, we...
In November 1996, the German national science foundation DFG (1997)
Sponsored Workshop, Manfred Denker, Stefan-m. Heinemann, Bernd Stratmann
multifractal intersection schemes, work in progress, 1997 [31] L. Olsen, Multifractal geometry. A survey, work in progress, 1997 [32] N. Patzschke, Self-conformal multifractals, preprint, 1996 [33]...
On the transfer operator for rational functions on the Riemann sphere (1996)
Manfred Denker, Feliks Przytycki, Mariusz Urbanski, Mariusz Urba Nski
: Let T be a rational function of degree 2 on the Riemann sphere. Denote L OE the transfer operator of a Holder-continuous function OE on its Julia set J = J(T ) satisfying P (T; OE) ? sup z2J OE(z)....
Characteristic Functions Of Random Variables Attracted To 1-Stable Laws (1995)
Jon. Aaronson, Manfred Denker, Where An R, Bn Are Constants
. The domain of attraction of a 1-stable law on R d is characterised by the expansions of the characteristic functions of its elements. x0 introduction Let X 1 ; X 2 ; : : : be R d -valued,...
Thesis (doctoral)--Friedrich-Alexander-Universität Erlangen-Nürnberg, 1972.
On the uniqueness of the maximum of the paths of random walks (0000)
Let @x"i be i.i.d. symmetric random variables with P(@x"i=3D1)=3D12 and denote by S"n their partial sums. We derive the distribution of the difference in the position of the last and first maximum of...
Resampling U-statistics using p-stable laws
Dehling, Herold, Denker, Manfred, Woyczynski, Wojbor A.
It is well known that symmetric statistics based on a kernel with finite second moment have a limit law which can be described by a multiple Wiener-Ito integral. However, if the kernel has less than...
Denker, Manfred, Puri, Madan L., Rösler, Uwe
A new approach to the asymptotic normality of the multivariate linear rank statistics is provided along with the Berry-Esséen and the Prohorov distance estimates for the remainder term in the...
On some limit laws for perturbed empirical distribution functions
Denker, Manfred, Puri, Madan L.
In this note, we establish the convergence properties for a broad class of random variables of the form Sn = [integral operator]Fn(Tn - s)[nu]n(ds) where Tn is some random variable, Fn is an...
Stable limit distributions for strongly mixing sequences
Denker, Manfred, Jakubowski, Adam
A necessary and sufficient condition for the weak convergence of partial sums of strongly mixing random sequences towards p-stable distributions is established and applied to recent work of Davis...
We show consistency and asymptotic normality of certain estimators for expected exponential growth rates under i.i.d. observations. These statistical functionals are of the formT(F)=[integral...
Local Limit Theorems For Gibbs-Markov Maps
. We prove conditional local limit theorems for Gibbs-Markov processes whose marginals are in the domain of attraction of a stable law with order in (0; 2). c fl1996. Introduction Given a R-valued...
On Hausdorff Measures And SBR Measures For Parabolic Rational Maps
If J is the Julia set of a parabolic rational map having Hausdorff dimension h 0 or 0 for some explicitly computable 0 > 0. x1 A dichotomy for SBR measures and Hausdor measures An analytic...
On the uniqueness of the maximum of the paths of random walks
Let @x"i be i.i.d. symmetric random variables with P(@x"i=3D1)=3D12 and denote by S"n their partial sums. We derive the distribution of the difference in the position of the last and first maximum of...