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Title:
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Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem
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Author:
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Gasull Embid, Armengol; Mañosa Fernández, Víctor
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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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We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a one-parameter family of counterexamples to the discrete Markus-Yamabe conjecture (La Salle conjecture); the study of the low periods of a Lotka-Volterra-type map; the existence of three limit cycles for a piece-wise linear planar vector field; a new counterexample of Kouchnirenko's conjecture;
and an alternative proof of the existence of a class of symmetric central configuration of the $(1+4)$-body problem. |
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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
-Periodic orbits
-Poincaré-Miranda Theorem
-Discrete and continuous dynamical systems
-Lotka-Volterra maps
-Thue-Morse maps
-Discrete Markus-Yamabe conjecture
-Kouchnirenko’s conjecture
-Limit cycles
-Planar
piecewise linear systems
-Central configurations
-Sistemes dinàmics diferenciables
-Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
-Classificació AMS::39 Difference and functional equations::39A Difference equations |
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Rights:
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Document type:
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Article - Draft
Report |
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