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Generators for topological entropy and expansiveness

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1070/rm1960v015n04abeh004095openalex-snapshot

NEW PROGRESS IN THE THEORY OF TRANSFORMATIONS WITH INVARIANT MEASURE

inferredcites →https://doi.org/10.1090/coll/036openalex-snapshot

Topological Dynamics

inferredcites →https://doi.org/10.1090/s0002-9904-1958-10223-2openalex-snapshot

Minimal sets: An introduction to topological dynamics

inferredcites →https://doi.org/10.1090/s0002-9904-1966-11498-2openalex-snapshot

Generators and strong generators in ergodic theory

inferredcites →https://doi.org/10.1090/s0002-9947-1965-0175106-9openalex-snapshot

Topological entropy

inferredcites →https://doi.org/10.1215/s0012-7094-68-03585-0openalex-snapshot

On ergodicity and mixing in topological transformation groups

inferredcites →https://doi.org/10.2140/pjm.1960.10.1163openalex-snapshot

On expansive homeomorphisms

inferredcites →https://doi.org/10.4064/fm-59-3-313-321openalex-snapshot

Expansive transformation semigroups of endomorphisms

inferredcites →https://doi.org/10.7146/math.scand.a-10776openalex-snapshot

Expansive Automorphisms in Compact Groups.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Basic Properties of Control Systems

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Introduction to Invariance Entropy

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Linear and Bilinear Systems

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General Estimates

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Controllability, Lyapunov Exponents, and Upper Bounds

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Escape Rates and Lower Bounds

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Examples

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Three Orderings on Repertoires

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Three Orderings on Repertoires

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Entropie und Erzeuger in dynamischen Verb�nden

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On dimension functions and topological Markov chains

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A characterization of symbolic cascades in terms of expansiveness and topological entropy

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Asymptotic properties of expansive homeomorphisms

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Homomorphisms of expansive transformation groups

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Periodic points under expansive homeomorphisms

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Expansive self-homeomorphisms of the cantor set

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Topological models for generators

inferred← citeshttps://doi.org/10.1007/bf01890606openalex-snapshot

Restricted topological entropy and expansive mappings

inferred← citeshttps://doi.org/10.1007/bf01890614openalex-snapshot

Expansiveness on locally compact spaces

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β-Transformations and symbolic dynamics

inferred← citeshttps://doi.org/10.1007/bfb0061735openalex-snapshot

The structure of compact connected groups which admit an expansive automorphism

inferred← citeshttps://doi.org/10.1007/s00574-019-00134-3openalex-snapshot

Measure Expansivity and Specification for Pointwise Dynamics

inferred← citeshttps://doi.org/10.1007/s10474-009-9081-2openalex-snapshot

Positively expansive homeomorphisms on compact metric spaces

inferred← citeshttps://doi.org/10.1007/s10699-020-09714-9openalex-snapshot

The Santa Fe Institute and Econophysics: A Possible Genealogy?

inferred← citeshttps://doi.org/10.1007/s10884-015-9502-6openalex-snapshot

Levels of Generalized Expansiveness

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Positively N-expansive Homeomorphisms and the L-shadowing Property

inferred← citeshttps://doi.org/10.1007/s11856-021-2246-6openalex-snapshot

Spectrum of weighted isometries: C*-algebras, transfer operators and topological pressure

inferred← citeshttps://doi.org/10.1007/s41980-020-00525-zopenalex-snapshot

Generalizations of Expansiveness in Non-Autonomous Discrete Systems

inferred← citeshttps://doi.org/10.1016/0016-660x(79)90029-1openalex-snapshot

F-Expansive transformation groups

inferred← citeshttps://doi.org/10.1016/0022-0396(72)90013-7openalex-snapshot

Expansive one-parameter flows

inferred← citeshttps://doi.org/10.1016/0040-9383(72)90033-xopenalex-snapshot

Some counter-examples in topological entropy

inferred← citeshttps://doi.org/10.1016/0167-2789(84)90254-9openalex-snapshot

Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics

inferred← citeshttps://doi.org/10.1016/j.jde.2019.05.001openalex-snapshot

Symbolic extensions and uniform generators for topological regular flows

inferred← citeshttps://doi.org/10.1016/j.jde.2019.09.052openalex-snapshot

Beyond topological hyperbolicity: The L-shadowing property

inferred← citeshttps://doi.org/10.1016/j.jde.2025.113469openalex-snapshot

Expansiveness, generators and Lyapunov exponents for finitely generated monoid actions

inferred← citeshttps://doi.org/10.1016/j.jfa.2024.110376openalex-snapshot

Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity

inferred← citeshttps://doi.org/10.1016/j.jmaa.2024.128989openalex-snapshot

Expansiveness, generators and Lyapunov exponents for random bundle transformations

inferred← citeshttps://doi.org/10.1016/j.jmaa.2026.130389openalex-snapshot

Gluing-orbit property, local stable/unstable sets, and induced dynamics on hyperspace

inferred← citeshttps://doi.org/10.1016/j.topol.2006.08.009openalex-snapshot

Positively expansive dynamical systems

inferred← citeshttps://doi.org/10.1016/j.topol.2016.04.016openalex-snapshot

Expansive homeomorphisms on non-Hausdorff spaces

inferred← citeshttps://doi.org/10.1016/j.topol.2018.09.004openalex-snapshot

Topologically sensitive dynamical systems

inferred← citeshttps://doi.org/10.1016/j.topol.2020.107075openalex-snapshot

Local stable sets of almost periodic points

inferred← citeshttps://doi.org/10.1016/j.topol.2020.107120openalex-snapshot

Expansivity on commutative rings

inferred← citeshttps://doi.org/10.1016/j.topol.2020.107577openalex-snapshot

Expansive systems on lattices

inferred← citeshttps://doi.org/10.1016/j.topol.2024.108880openalex-snapshot

Positively ep-expansive dynamical systems

inferred← citeshttps://doi.org/10.1016/j.topol.2026.109784openalex-snapshot

Symbolically expansive induced systems

inferred← citeshttps://doi.org/10.1016/s0079-8169(08)60742-4openalex-snapshot

Bibliography

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Chapter 15 Topological Dynamics

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References

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Entropy of graphs, semigroups and groups

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Self-similar hyperbolicity

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A Further Result on Extending Expansive Homeomorphisms

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Entropy-Expansive Maps

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A geometric framework for asymptoticity and expansivity in topological dynamics

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Strongly Isomorphic Symbolic Extensions for Expansive Topological Flows

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Agent-based modelling and economic complexity: a diversified perspective

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A generalization of the cellular automata rule-30 cryptoscheme

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Asymptotic Properties of G‐Expansive Homeomorphisms on a Metric G‐Space

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On Nonautonomous Discrete Dynamical Systems

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Positively expansive homeomorphisms of compact spaces

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Every compact metric space that supports a positively expansive homeomorphism is finite

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ENTROPY MAPS FOR MEASURE EXPANSIVE HOMEOMORPHISM

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Modelling expansion in real flows

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Extension of flows via discontinuous functions

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On the metrizability of TVS-cone metric spaces

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Markov Partitions for Axiom A Diffeomorphisms

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A Variational Principle for the Pressure of Continuous Transformations

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Invariants Of Uniform Conjugacy On Uniform Dynamical System

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Markov subshifts and realization of β-expansions

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Extensions of expansive dynamical systems

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On the multifractal spectrum of weighted Birkhoff averages

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Distortion and the automorphism group of a shift

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Fractal Weyl law for open quantum chaotic maps

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GH-stability and Spectral Decomposition for Group Actions

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Various Non-autonomous Notions for Borel Measures

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Nonstandard Expansiveness

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Invariants of topological G-conjugacy on G-spaces

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