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On the Entropy of Continuous Flows with Uniformly Expansive Points and the Globalness of Shadowable Points with Gaps
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a...
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Some Results on Shadowing and Local Entropy Properties of Dynamical Systems
We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient...
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A Spectral Representation for the Entropy of Topological Dynamical Systems
In this paper, we follow an approach which considers the entropy of a dynamical system as a linear operator. We assign a linear operator on L p spaces...
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Variational Principle of Topological Pressure of Free Semigroup Actions for Subsets
In this paper, we investigate the relation between topological pressure of free semigroup actions for non-compact sets proposed by **ao and Ma (J...
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Topological and Geometric Rigidity for Spaces with Curvature Bounded Below
We briefly survey two results asserting topological and geometric rigidity of certain classes of spaces with curvature bounded below: The Borel...
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Stitch Fix for Mapper and Topological Gains
The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data....
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G-index, topological dynamics and the marker property
Given an action of a finite group G on a topological space, we can define its index. The G -index roughly measures a size of the given G -space. We...
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The Symbolic Extension Theory in Topological Dynamics
In this survey we will present the symbolic extension theory in topological dynamics, which was built over the past twenty years.
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On the entropy of Hilbert geometries of low regularities
We compare the regularity of the boundary of a convex set with the value of its Finslerian volume entropy. The main result states that the volume...
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C0-gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces
Let Σ be a surface equipped with an area form. There is a long-standing open question by Katok, which, in particular, asks whether every entropy-zero...
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Topological Drawings Meet Classical Theorems from Convex Geometry
In this article we discuss classic theorems from Convex Geometry in the context of topological drawings and beyond. In a simple topological drawing...
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Topological Stability and Pseudo-orbit Tracing Property for Homeomorphisms on Uniform Spaces
In this paper, we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces. We introduce the...
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Möbius orthogonality of sequences with maximal entropy
We prove that strongly b -multiplicative functions of modulus 1 along squares are asymptotically orthogonal to the Möbius function. This provides...
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Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space
We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian...
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Rigidity of Entropy Spectra for One-Parameter Family of Polynomials
In this paper, we consider entropy spectra of Markov measures on topological Markov shifts. For a Markov measure on a shift, using the description of...
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