Shadowing in dynamical systems: theory and applications


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In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough ...

Shadowing in Dynamical Systems: Theory and Applications 2000, Springer, Dordrecht, Netherlands

ISBN-13: 9780792361794

2000 edition