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.
Upper bounds on measure theoretic tail entropy for dominated splittings
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abstract
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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2019 1verdicts
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A countable partition for singular flows, and its application on the entropy theory
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.