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The central limit theorem for dynamical systems

100%

Denker M.

tom 23

nr 1

33-62

A note on the construction of nonsingular Gibbs measures

84%

Denker M. , Yuri M.

nr 2

377-383

We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.

Markov partitions for fibre expanding systems

84%

Denker M. , Holzmann H.

Colloquium Mathematicum

2008

tom 110

nr 2

485-492

Fibre expanding systems have been introduced by Denker and Gordin. Here we show the existence of a finite partition for such systems which is fibrewise a Markov partition. Such partitions have direct applications to the Abramov-Rokhlin formula for relative entropy and certain polynomial endomorphisms of ℂ².

Jordan tori and polynomial endomorphisms in $ℂ^2$

84%

Denker M. , Heinemann S. M.

nr 2-3

139-159

For a class of quadratic polynomial endomorphisms $f: ℂ^2 → ℂ^2$ close to the standard torus map $(x,y) → (x^2,y^2)$, we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).

Conformal measures for rational functions revisited

67%

Denker M. , Daniel Mauldin R. , Nitecki Z. , Urbański M.

nr 2-3

161-173

We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.

On the uniqueness of equilibrium states for piecewise monotone mappings

67%

Denker M. , Keller G. , Urbański M.

nr 1

27-36