Sergej Ju. Piljugin Bücher

Reviews of 1rst edition: __„A book based on 30 years of teaching experience and therefore didactically and logically composed.“ In: Enseignement Mathematique 2/2012 __"In the reviewer's opinion, in view of the numerical study of nonlinear systems, this book would be very useful to, in particular, engineers, physicists and economists who want to study the systems in a numerical way.„ Mathematical Reviews __“The main strength of this book is that the author includes complete proofs of results that other publications frequently leave to the reader. […] Altogether, this text is for serious readers that would like a clean and rigorous introduction to the results and methods of proof in dynamical systems. It would make a valuable addition as a reference text to the collection of any academician working in related fields." Zentralblatt für Mathematik

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 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.