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Upper bounds on measure theoretic tail entropy for dominated splittings

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arxiv 1901.01694 v1 pith:B4EOWPYN submitted 2019-01-07 math.DS

Yongluo Cao , Gang Liao , Zhiyuan You This is my paper · ORCID
classification math.DS
keywords entropyupperdominatedsplittingstailapplicationboundsdifferentiable
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For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy in various settings with domination.

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  1. A countable partition for singular flows, and its application on the entropy theory

    math.DS 2019-08 conditional novelty 7.0 of 10

    Hyperbolic singularities can be surrounded by a finite-entropy countable partition whose atoms control scaled tubular neighborhoods, yielding entropy formulas and upper semi-continuity away from tangencies.

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