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Dimension and measures on sub-self-affine sets
We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological...
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Regular interval Cantor sets of S 1 and minimality
It is known that not every Cantor set of S 1 is C 1 -minimal. In this work we prove that every member of a subfamily of what we here call regular...
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The relation of dimension, entropy and Lyapunov exponent in random case
We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure...
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New examples of Cantor sets in S1 that are not C1-minimal
Although every Cantor subset of the circle ( S 1 ) is the minimal set of some homeomorphism of S 1 , not every such set is minimal for a C 1 diffeomorphism...
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Real analyticity of Hausdorff dimension for higher dimensional hyperbolic graph directed Markov systems
In this paper we prove that the Hausdorff dimension function of the limit sets of strongly regular, hyperbolic, conformal graph directed Markov...
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Analytic Multifunctions, Holomorphic Motions and Hausdorff Dimension in IFSs
We study iterated function systems of contractions which depend holomorphically on a complex parameter λ. We first restrict our attention to systems...
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Stable intersections of affine cantor sets
We construct open sets of pairs of affine Cantor sets ( K , K ′) with the simplest possible combinatorics (i. e., defined by two affine increasing maps)...
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On Dimension and Metric Properties of Trajectory Attractors
We study metric properties of trajectory attractors for infinite-dimensional dissipative systems. Under natural conditions we show that in the...
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The Rényi dimension of a conformal measure for a piecewise monotonic map of the interval
We consider a continuous piecewise monotonic transformation <Emphasis Type=”Italic”>T</Emphasis> on the interval, which is expanding, and an...
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Dimension de la mesure d’équilibre d’applications méromorphes
Let ƒ be a dominating meromorphic self-map of a compact Kähler manifold. Assume that the topological degree of ƒ is larger than the other dynamical...
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A note on the relationship of pointwise dimensions of an invariant measure and its natural extension
In this note we present an estimate on the relationship of lower pointwise dimensions of an invariant measure of a Lipschitz map on a compact metric...
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Relations Between Some Quantities in Classical Thermodynamics and Abstract Dynamics. Beyond Hyperbolicity
Formal relationships among statistical mechanics, multifractal analysis, and dynamical systems with weaker conditions than the existence of Markov...
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The entropy theory of symbolic extensions
Fix a topological system ( X , T ), with its space K ( X , T ) of T -invariant Borel probabilities. If ( Y , S ) is a symbolic system (subshift) and ϕ:( Y , S )→( X , T )...
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The reconstruction theorem for endomorphisms
The reconstruction theorem deals with dynamical systems which are given by a map φ : M → M together with a read out function ƒ : M → ℝ. Restricting...
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The Basic Attractor of the Viscous Moore-Greitzer Equation
The basic attractor of a nonlinear partial differential equation is the part of the global attractor that attracts a prevalent set in phase space....