Perturbations of mappings with periodic repellers

DOI10.1016/0362-546X(83)90107-4zbMath0504.58030MaRDI QIDQ4741450

Frederick R. Marotto, Thomas D. Rogers

Publication date: 1983

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

chaotic behaviourHenon mappingsnapback repellercubic mappingtransverse homoclinic orbitperiodic repellers

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (9)

Dynamics of a two-parameter family of maps of the interval ⋮ On the generalized successive approximations method ⋮ Critical sets and unimodal mappings of the square ⋮ An extension of Chu-Moyer's theorem to two variable functions ⋮ Linear Generalized Synchronization of Spatial Chaotic Systems ⋮ Rarity and chaos ⋮ Remarks on multiparameter mappings: controlled-parameter and threshold maps ⋮ Homoclinic shadowing ⋮ The evolution of crisis: bifurcation and demise of a snapback repeller

Cites Work

• Chaotic behavior in the Henon mapping
• A two-dimensional mapping with a strange attractor
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Stable and Random Motions in Dynamical Systems
• Topological horseshoe and numerically observed chaotic behaviour in the Henon mapping
• Differentiable dynamical systems
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