Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Shadowing in a Neighbourhood of a Separatrix

Author(s):

Alexey Alexeyevich Petrov

Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia

al.petrov239@gmail.com

Abstract:

We consider a model example of a plane diffeomorphism with two hyperbolic fixed points connected by a separatrix. We show that in a tubular neighborhood of the separatrix a pseudotrajectory satisfying some additional condition on the smallness of one-step errors can be shadowed by an exact trajectory.

References:

1. W. de Melo, Moduli of stability for diffeomorphisms, Topology 19 (1980) 9-21
2. O. Plamenevskaya, Weak shadowing for two dimensional diffeomor-phisms, Vestnik St. Petersburg Univ. Math, 31, 49–56 (1999)
3. S. Yu. Pilyugin, Shadowing in dynamical systems, Lecture Notes in Mathematics, Springer 1706 (1999)
4. A. A. Petrov, S. Yu. Pilyugin, Shadowing near nonhyperbolic fixed points, Discrete and Continuous Dynamical Systems - Series A (submitted)

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