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.