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Bowen–Walters expansiveness for semigroups of linear operators

Part of: Smooth dynamical systems: general theory Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  18 April 2022

J. LEE  and
C. A. MORALES Open the ORCID record for C. A. MORALES [Opens in a new window]
J. LEE
Affiliation:
Department of Mathematics, Chonnam National University, Gwangju 61186, Republic of Korea (e-mail: jihoon@jnu.ac.kr)
C. A. MORALES*
Affiliation:
Instituto de Matematica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 68530, Brazil
*
e-mail: morales@impa.br
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Abstract

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.

Keywords

expansive flowpositively expansive semigroupBanach spacegenerator

MSC classification

Primary: 47D03: Groups and semigroups of linear operators
Secondary: 37C10: Vector fields, flows, ordinary differential equations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 6 , June 2023 , pp. 1942 - 1951
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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