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q-invariance Entropy for Control Systems
We introduce the notions of q -invariance entropy and q -metric invariance entropy for control systems by Carathéodory–Pesin structures. We obtain some...
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Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions
We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability...
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Nonlinear fractal interpolation curves with function vertical scaling factors
In this paper we present a method to generate new fractal interpolation curves. We ensure that attractors of nonlinear iterated function systems...
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Local stable and unstable sets for positive entropy C1 dynamical systems
For any C 1 diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the...
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Dimension of slices through fractals with initial cubic pattern
In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R n generated from an initial cube pattern...
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Points with maximal Birkhoff average oscillation
Let f : X → X be a continuous map with the specification property on a compact metric space X . We introduce the notion of the maximal Birkhoff average...
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About C 1-minimality of the hyperbolic Cantor sets
In this work we prove that a C 1+ α -hyperbolic Cantor set contained in S 1 that is close to an affine Cantor set is not C 1 -minimal.
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On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions
We study the topology of a set naturally arising from the study of β -expansions. After proving several elementary results for this set we study the...
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Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure
Let { S i }
i =1 l be an iterated function system (IFS) on ℝ d with attractor K. Let π be the canonical projection. In this paper, we define a new... -
Frequencies of digits under trigonometric perturbations
We study the Hausdorff dimension of a class of sets of real numbers defined in terms of frequencies of digits in some integer base m , with the...
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Level sets of multiple ergodic averages
We propose to study multiple ergodic averages from multifractal analysis point of view. In some special cases in the symbolic dynamics, the Hausdorff...
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Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces
We extend the Besicovitch-Federer projection theorem to transversal families of map**s. As an application we show that on a certain class of...
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Unstable directions and fractal dimension for skew products with overlaps in fibers
A unique feature of smooth hyperbolic non-invertible maps is that of having different unstable directions corresponding to different prehistories of...
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Simultaneously non-convergent frequencies of words in different expansions
We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already...
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On the Lyapunov spectrum for rational maps
We study the dimension spectrum for Lyapunov exponents for rational maps on the Riemann sphere.
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On the variational principle for the topological pressure for certain non-compact sets
Let ( X, d, T ) be a dynamical system, where ( X, d ) is a compact metric space and T : X → X is a continuous map. We assume that the dynamical system...