Transversal homoclinic points and hyperbolic sets for non-autonomous maps II
Copyright policy )Transversal homoclinic points and hyperbolic sets for non-autonomous maps II
The paper continues the study performed by the author in [ibid. 39, No. 4, 518--549 (1988; Zbl 0672.58034)] where the concept of hyperbolic sets and transversal homoclinic points to non-autonomous systems has been generalized. The main result of this work is to exhibit conditions which imply the existence of transverse homoclinic orbits for such systems. In order, the method of Mel'nikov is generalized and the theory developed is applied to almost perturbed differential equations.
- ETH Zurich Switzerland
transverse homoclinic orbits, existence, Topological dynamics of nonautonomous systems, almost perturbed differential equations, homoclinic points, Dynamical systems with hyperbolic orbits and sets, Homoclinic and heteroclinic orbits for dynamical systems, Melnikov method, Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics, hyperbolic sets
transverse homoclinic orbits, existence, Topological dynamics of nonautonomous systems, almost perturbed differential equations, homoclinic points, Dynamical systems with hyperbolic orbits and sets, Homoclinic and heteroclinic orbits for dynamical systems, Melnikov method, Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics, hyperbolic sets
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