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2 results

Bowen–Walters expansiveness for semigroups of linear operators
Part of
- Groups and semigroups of linear operators, their generalizations and applications
- Smooth dynamical systems: general theory
J. LEE, C. A. MORALES
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 6 / June 2023

Published online by Cambridge University Press:

18 April 2022, pp. 1942-1951

Print publication:

June 2023
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We define positively expansive semigroups of linear operators on Banach spaces. We characterize these semigroups in terms of the point spectrum of the infinitesimal generator. In particular, we prove that a positively expansive semigroup is neither uniformly bounded nor equicontinuous. We apply our results to the Lasota equation.

Geodesic Flows Modelled by Expansive Flows
Part of
Katrin Gelfert, Rafael O. Ruggiero
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 1 / February 2019

Published online by Cambridge University Press:

28 August 2018, pp. 61-95
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Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.

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2 results

Bowen–Walters expansiveness for semigroups of linear operators

Geodesic Flows Modelled by Expansive Flows