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Chaotic behaviour in simple dynamical systems. (English) Zbl 0715.58024

From the authors’ abstract: “A description is given of the chaotic behaviour generated by a transversal homoclinic point of a plane map. A proof of Smale’s theorem via the shadowing property of hyperbolic sets is provided. The result is related to certain plane periodic systems of ODE’s like the periodically perturbed pendulum equation. To this end the so-called method of Melnikov is derived.”
Reviewer: K.Brod

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37D15 Morse-Smale systems
34D45 Attractors of solutions to ordinary differential equations
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