## Shadowing in Dynamical SystemsThis 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 shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods. |

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### Contents

1 | |

Topologically Stable Structurally Stable and Generic | 103 |

Systems with Special Structure | 173 |

Numerical Applications of Shadowing 219 | 218 |

References | 259 |

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### Common terms and phrases

analog Anosov apply assume Banach spaces basic set completes the proof consider coordinates corresponding d-pseudotrajectory deduce define Definition denote diffeomorphism differential equations dynamical system e)-shadowed exist numbers finite fixed point flows following property following statement follows from Lemma function global attractor hence holds homeomorphism hyperbolic fixed points hyperbolic set II(p implies inequality Let us show linear subspaces Lipschitz constant LpSP Lyapunov Lyapunov exponents Math matrix metric metric space natural number nonwandering nonwandering set norm Obviously periodic path point a e POTP proof of Theorem pseudo-orbit r-interval Remark satisfies sequence of mappings Shadowing Lemma shadowing property shadowing results solution structurally stable structurally stable diffeomorphisms subbundle Subsect Take a point topologically stable uniformly unique unstable manifolds vºl wººl