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Content available

The central limit theorem for dynamical systems

100%
Denker M.
Banach Center Publications
|
1989
|
tom 23
|
nr 1
33-62
2
Content available remote

Jordan tori and polynomial endomorphisms in $ℂ^2$

84%
Denker M., Heinemann S. M.
Fundamenta Mathematicae
|
1998
|
tom 157
|
nr 2-3
139-159
EN
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).
3
Content available remote

Markov partitions for fibre expanding systems

84%
Denker M., Holzmann H.
Colloquium Mathematicum
|
2008
|
tom 110
|
nr 2
485-492
EN
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.
4
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A note on the construction of nonsingular Gibbs measures

84%
Denker M., Yuri M.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 2
377-383
EN
We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
5
Content available remote

Dirichlet forms on quotients of shift spaces

68%
Denker M., Imai A., Koch S.
Colloquium Mathematicum
|
2007
|
tom 107
|
nr 1
57-80
EN
We define thin equivalence relations ∼ on shift spaces $𝒜 ^{∞}$ and derive Dirichlet forms on the quotient space $Σ = 𝒜 ^{∞}/∼$ 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.
6
Content available remote

Conformal measures for rational functions revisited

68%
Denker M., Daniel Mauldin R., Nitecki Z., Urbański M.
Fundamenta Mathematicae
|
1998
|
tom 157
|
nr 2-3
161-173
EN
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.
7
Content available remote

On the uniqueness of equilibrium states for piecewise monotone mappings

68%
Denker M., Keller G., Urbański M.
Studia Mathematica
|
1990
|
tom 97
|
nr 1
27-36
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