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Title:
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A Route to chaos in the Boros–Moll map
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Author:
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Gardini, Laura; Mañosa Fernández, Víctor; Sushko, Iryna
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
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Abstract:
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The Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros–Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros–Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros–Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
-Differentiable dynamical systems
-Chaotic behavior in systems
-Boros–Moll map
-chaotic set
-critical line
-homoclinic bifurcation
-noninvertible planar map
-snapback repellor
-Sistemes dinàmics diferenciables
-Caos (Teoria de sistemes)
-Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
-Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory |
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Rights:
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Document type:
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Article - Submitted version
Article |
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