Homoclinical structures in nonautonomous systems: Nonautonomous chaos

DOI10.1063/1.165887zbMath1055.37552OpenAlexW1980468513WikidataQ52417856 ScholiaQ52417856MaRDI QIDQ4526237

L. P. Shil'nikov, Lev M. Lerman

Publication date: 16 January 2001

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

Full work available at URL: https://doi.org/10.1063/1.165887

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Topological dynamics of nonautonomous systems (37B55)

Related Items (12)

Truncated fractal basin boundaries in the pendulum with nonperiodic forcing ⋮ Nonautonomous systems with transversal homoclinic structures under discretization ⋮ Melnikov processes and chaos in randomly perturbed dynamical systems ⋮ Nonautonomous gradient-like vector fields on the circle: classification, structural stability and autonomization ⋮ Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields ⋮ Nonuniform exponential dichotomies and Lyapunov functions ⋮ Invariant manifolds and control of hyperbolic trajectories on infinite- or finite-time intervals ⋮ On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation ⋮ Replication of chaos ⋮ On the omega-limit sets of planar nonautonomous differential equations with nonpositive Lyapunov exponents ⋮ The weak Smale horseshoe and mean hyperbolicity ⋮ REMARKS ON SKEW PRODUCTS OVER IRRATIONAL ROTATIONS

Cites Work

• Chaos in almost periodic systems
• Homoclinic orbits in Hamiltonian systems
• Chaotic solutions of systems with almost periodic forcing
• Exponential dichotomies and transversal homoclinic points
• Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus
• Differentiable dynamical systems
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
• ON A POINCARÉ-BIRKHOFF PROBLEM

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