dc.contributor.author
Alsedà, L.
dc.contributor.author
Bordignon, L.
dc.contributor.author
Groisman, J.
dc.date.accessioned
2025-01-22T09:29:13Z
dc.date.available
2025-01-22T09:29:13Z
dc.date.issued
2024-07-30
dc.identifier.uri
http://hdl.handle.net/2072/480069
dc.description.abstract
Transitivity, the existence of periodic points, and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that, for every graph that is not a tree and any epsilon > 0, there exist (complicated) totally transitive maps (then with cofinite set of periods) such that the topological entropy is smaller than epsilon (simplicity). To numerically measure the complexity of the set of periods, we introduce a notion of the boundary of cofiniteness. Larger boundary of cofiniteness corresponds to a simpler set of periods. We show that, for any continuous circle maps of degree one, every totally transitive (and, hence, robustly complicated) map with small topological entropy has arbitrarily large (simplicity) boundary of cofiniteness.
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dc.description.sponsorship
The authors have been partially supported by the Spanish Ministerio de Economia y Competitividad (GrantNo. MTM2014-52209-C2-1-P) and the Spanish Ministerio de Economia, Industria y Competitividad (Grant No. MTM2017-86795-C3-1-P). Lluis Alseda acknowledges financial support from the Spanish Ministerio de Ciencia en Innovacion (Grant No. PID2020-118281GB-C31), from the Spanish Ministerio de Economia y Competitividad (Grant No. MDM-2014-0445) within the Maria de Maeztu excellence program, and the Spanish State Research Agency, through the Severo Ochoa and Mar & imath;a de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The second author has been partially supported by the CNPq-Brasil. The third author has been partially supported by the CSIC group 618-Uruguay.
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dc.format.extent
76 p.
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dc.relation.ispartof
Ukrainian Mathematical Journal
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dc.rights
Attribution-NonCommercial 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by-nc/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Entropy
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dc.title
Topological Entropy, Sets of Periods, and Transitivity for Circle Maps
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/submittedVersion
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dc.identifier.doi
10.1007/s11253-024-02305-y
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
