Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism

DOI10.1007/s00332-024-10079-7MaRDI QIDQ6624014

Ernest Fontich, Antonio Garijo, Xavier Jarque

Publication date: 24 October 2024

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

basin of attractionsymbolic dynamicsperiodic pointshomoclinic connectionstable and unstable manifoldsecant map

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Invariant manifold theory for dynamical systems (37D10) Dynamical systems with hyperbolic orbits and sets (37D05) Symbolic dynamics (37B10) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Cites Work

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• Poincaré - Melnikov - Arnold method for analytic planar maps
• Dynamics of the Secant map near infinity
• Global dynamics of the real secant method
• The secant method for root finding, viewed as a dynamical system

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