dc.contributor.author
Fontich, E.
dc.contributor.author
Garijo, A.
dc.contributor.author
Jarque, X.
dc.date.accessioned
2025-01-08T09:39:23Z
dc.date.available
2025-01-08T09:39:23Z
dc.date.issued
2024-09-11
dc.identifier.uri
http://hdl.handle.net/2072/480010
dc.description.abstract
In this paper, we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which come out as a truncated map governing the local dynamics near a critical period three-cycle associated with the Secant map. Using Moser’s version of Birkhoff–Smale’s theorem, we prove that the boundary of the basin of attraction of the origin contains a Cantor-like invariant subset such that the restricted dynamics to it is conjugate to the full shift of N-symbols for any integer N ≥ 2 or infinity.
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dc.description.sponsorship
The first author is supported by grant PID2021-125535NB-I00 funded MICIU/AEI/10.13039/501100011033, FEDER/EU. The second and third authors are supported by grant PID2020-118281GB-C32(33) funded MICIU/AEI/10.13039/501100011033, FEDER/EU. Moreover, the second author is supported by Generalitat de Catalunya 2021SGR-633. We want to thank the Thematic Research Programme Modern holomorphic dynamics and related fields, , Excellence Initiative-Research University programme at the University of Warsaw. Finally, this work has also been funded through the Maria de Maeztu Program for Centers and Units of Excellence in R&D, grant CEX2020-001084-M funded by MICIU/AEI/10.13039/501100011033/FEDER,UE.
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dc.format.extent
32 p.
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dc.relation.ispartof
Journal of Nonlinear Science
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dc.rights
(c) 2024 The Author(s)
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dc.rights
Attribution 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject.other
Secant map
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dc.subject.other
Basin of attraction
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dc.subject.other
Stable and unstable manifold
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dc.subject.other
Homoclinic connection
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dc.subject.other
Periodic points
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dc.subject.other
Symbolic dynamics
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dc.title
Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1007/s00332-024-10079-7
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
