Lipschitz Shadowing in Piecewise Linear Mappings
Author(s):
Sergei Yurievich Pilyugin
Doctor of Phys. and Math.Science,
Professor of Higher Geometry Dept,
St.Petersburg State University
sp@sp1196.spb.edu
Anastasia Aleksandrovna Rodionova
Assistant Prof. of Differential Equation Dept.
St.Petersburg State University
Abstract:
We study a continuous mapping f of the n-dimensional Euclidean space
that is linear and hyperbolic on a family of sets {Gl} with disjoint interiors.
We study finite pseudotrajectories of the mapping f such that their long
enough blocks belong to the sets {Gl} while their blocks not belonging to
{Gl} are of bounded length.
We obtain sufficient conditions under which such pseudotrajectories are
Lipschitz shadowed by exact trajectories of the mapping f (and the
Lipschitz constant does not depend on the total length of the
pseudotrajectory).
The principal novelty is the introduced analog of the transversality
condition.
Keywords
- Dynamical system
- hyperbolicity
- shadowing
- transversality
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