Almost-Topological Representation Theorems for Dynamical Systems.
Some New Examples of Gibbs Measures.
On Strict Ergodicity.
On Unitary Operators Inducing Measure-Preserving Transformations.
The central limit theorem for dynamical systems
Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points.
A Short Proof of a Theorem of Ruelle.
A note on the construction of nonsingular Gibbs measures
We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
Jordan tori and polynomial endomorphisms in
For a class of quadratic polynomial endomorphisms close to the standard torus map , 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).
Markov partitions for fibre expanding systems
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.
Eine Bemerkung zur topologischen Entropie.
On the uniqueness of equilibrium states for piecewise monotone mappings
Dirichlet forms on quotients of shift spaces
We define thin equivalence relations ∼ on shift spaces and derive Dirichlet forms on the quotient space in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.
The almost sure invariance principle for the empirical process of U-statistic structure
Conformal measures for rational functions revisited
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.
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