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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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Preprint |
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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 the convergence of them. In the paper, we study the dynamics of a one-parameter family of maps which unfolds 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. Special attention is devoted to 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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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 system
-Attractors
-bifurcations
-Boros-Moll map
-chaos
-Landen transformations
-periodic orbits.
-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 - Draft
Report |
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