Título:
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A route to chaos in the Boros-Moll map
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Autor/a:
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Gardini, Laura; Mañosa Fernández, Víctor; Sushko, Iryna
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
Abstract:
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Preprint |
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. |
Materia(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 |
Derechos:
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Tipo de documento:
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Artículo - Borrador Informe |
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