Random and Computational Dynamics

Volume 1    ISBN-10: 1-60133-012-X; ISBN-13: 978-1-60133-012-3

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Semi-Hyperbolicity and Bi-Shadowing
By Phil Diamond, Peter Kloeden, Victor Kozyakin and Alexei Pokrovskii

Semi-hyperbolicity extends the classical concept of hyperbolicity for diffeomorphisms to noninvertible Lipschitz mappings on sets that need not be invariant. Moreover, the stable and unstable manifolds need to be mapped only approximately onto their counterparts.

Semi-hyperbolic mappings are bi-shadowing, i.e., they also satisfy a converse form of shadowing in which the pseudo-orbits are not arbitrary but are the true orbits of admissible classes of approximating mappings.

The theory of these concepts is developed systematically in this monograph and illustrated through applications of nonsmooth systems including those with delays and hysteresis, as well as numerical approximations. Setvalued mappings are also considered.