Publication:
Asymptotic expansivity
Asymptotic expansivity
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Date
2022
Authors
Lee K.
Morales C.A.
Villavicencio H.
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Academic Press Inc.
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Abstract
We study continuous maps of metric spaces for which two nearby orbits are asymptotic (termed asymptotically expansive for short). We also analyze the bi-asymptotically expansive homeomorphisms namely asymptotically expansive homeomorphisms with asymptotically expansive inverse. Indeed, we obtain necessary and sufficient conditions for asymptotic expansivity, characterize the asymptotically expansive homeomorphisms of the circle, prove a spectral decomposition theorem and estimate the entropy through the growth rate of the periodic orbits. © 2021 Elsevier Inc.
Description
KL was partially supported by NRF grant No. 2018R1A2B3001457 . CAM was partially supported by CNPq -Brazil No. 307776/2019-0 and the NRF Brain Pool Grant No. 2020H1D3A2A01085417 . HV was partially supported by Universidad Nacional de Ingeniería P-CC-2021-000666 , FC-PF-33-2021 and Fondecyt-Concytec contract 100-2018 .
Keywords
Topological entropy,
Asymptotically expansive,
Expansive map