Shadowing property: State of art and perspectives

  • Sergey Tikhomirov (MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)


We consider a dynamical system generated by a diffeomorphism or a vector field. The shadowing problem is related to the following question: Under which conditions, for any pseudotrajectory of a dynamical system there exists a close trajectory? This notion is important for stability theory and for theoretical motivation of numerical simulations.

It is well known that a dynamical system has shadowing property in a neighborhood of a hyperbolic set. In fact it is informally believed that almost only hyperbolic systems have shadowing. While construction of non-hyperbolic example with shadowing is easy, converting this informal feeling to rigorous statements is more tricky.

I give an overview of main results in this theory and describe perspectives for future research. In particular problems relating shadowing to skew products and stochastic stability.

11.05.10 19.05.20

Dynamical Systems Seminar

MPI for Mathematics in the Sciences Live Stream

Katharina Matschke

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