This article reviews the application of various notions from the theory of dynamical systems
to the analysis of numerical approximation of initial value problems over long-time intervals …

This book is an introduction to the theory of shadowing of approximate trajectories in
dynamical systems by exact ones. This is the first book completely devoted to the theory of …

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows,
with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the …

Numerical simulations of mathematical models can suggest that the models are chaotic. For
example, one can compute an orbit and its associated finite-time Lyapunov exponents, and …

In this paper, we investigate the impact of numerical instability on the reliability of sampling,
density evaluation, and evidence lower bound (ELBO) estimation in variational flows. We …

We prove that the chain-transitive sets of C 1-generic diffeomorphisms are approximated in
the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense …

Shadowing is generic Page 1 Topology and its Applications 97 (1999) 253–266 Shadowing is
generic 6 S.Yu. Pilyugin, OB Plamenevskaya Department of Mathematics and Mechanics …

We study weak and orbital shadowing properties of dynamical systems related to the
following approach: we look for exact trajectories lying in small neighborhoods of …

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in
the study of dynamical systems. In this paper we prove that there is a deep and fundamental …

We prove that the shadowing property does not hold for diffeomorphisms in an open and
dense subset of the set of C1-robustly non-hyperbolic transitive diffeomorphisms (ie …