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Weighted Entropy Formulae on Feldman-Katok Metric
In this paper, we prove that the weighted topological entropy defined by FK metric and Bowen metric are equal. Moreover, we establish a Brin-Katok...
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Katok’s Entropy Formula of Unstable Metric Entropy for Partially Hyperbolic Diffeomorphisms
Katok’s entropy formula is an important formula in entropy theory. It plays significant roles in large deviation theories, multifractal analysis,...
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Topological Entropy and Metric Entropy for Regular Impulsive Semiflows
Several notions of topological entropy for non necesarily continuous semiflows were introduced because the classical notion of topological entropy...
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Topological Complexity: Entropy Point, Metric Mean Dimension in Control Systems
We introduce two new notions to describe the topological complexity of control systems. We first introduce a notion called entropy point to...
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Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks
In this article, we study approximation properties of the variation spaces corresponding to shallow neural networks with a variety of activation...
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Uniform approximation rates and metric entropy of shallow neural networks
We study the approximation properties of the variation spaces corresponding to shallow neural networks with respect to the uniform norm....
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Functional Quantization, Small Ball Probabilities, Metric Entropy and Series Expansions for Gaussian Processes
This chapter provides some abstract tools in order to determine the rate of decay of the functional quantization error of Gaussian processes and...
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On Variational Principles of Metric Mean Dimension on Subsets in Feldman–Katok Metric
In this paper, we studied the metric mean dimension in Feldman–Katok (FK for short) metric. We introduced the notions of FK-Bowen metric mean...
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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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Metric Versus Topological Receptive Entropy of Semigroup Actions
We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by...
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Polynomial Entropy of Amenable Group Actions for Noncompact Sets
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability...
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The Categorical Basis of Dynamical Entropy
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical...
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Entropy collapse versus entropy rigidity for Reeb and Finsler flows
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arbitrarily small topological entropy. In contrast,...
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Sharp Baire Classification of Local Entropy of Parametric Families of Dynamical Systems
AbstractWe consider a parametric family of dynamical systems defined on a locally compact metric space and continuously dependent on a parameter from...
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Some Variational Principles for the Metric Mean Dimension of a Semigroup Action
In this manuscript, we show that the metric mean dimension of a semigroup action satisfies three variational principles: (a) in our first result, we...
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Topological Entropy, Topological Pressure and Topological Pseudo Entropy of Iterated Function Systems on Uniform Spaces
In this paper, we introduce the notions of topological entropy, topological pressure and topological pseudo-entropy of iterated function systems( IFS )...
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Entropy: Discrete Case
The main character of this chapter is the entropy function ( 1.2.9 ),...
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Entropies of non-positively curved metric spaces
We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of...
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Some Properties of the Topological Entropy of a Family of Dynamical Systems Defined on an Arbitrary Metric Space
AbstractWe consider a family of dynamical systems defined on a noncompact metric space and continuously depending on a parameter varying in some...