A First Course in Dynamics: with a Panorama of Recent Developments 1st Edition by Boris Hasselblatt (PDF)

Description

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book could potentially be an excellent book with a few new editions. However, this current version (published in 2003) has too many minor errors (both mathematical and typographical) that turn what should be an enjoyable experience into a frustrating search for “what the author(s) really meant.” In addition, no errata document seems to be available that addresses them all. In one place, the authors use a forward slash with set-builder notation, rather than the standard vertical bar or colon…who does that? In addition, there is at least one “solution” given in the back, which (in my opinion) is aberrant. Although, I will say that the problems are challenging and the hints and solutions section is, for the most part, a big plus. One last issue is that a few terms (well, at least one: semiorbit) seem to be used before or without being defined. Maybe semiorbit was defined in the exercises somewhere, but I certainly could not find. I didn’t see it in the index, and it didn’t appear to be defined in the vicinity of the page where the term orbit is defined. After a little searching and thinking, one can glean what a semiorbit is, but the reader shouldn’t have to do this (especially when reading a math textbook). Again, let me qualify by saying that I couldn’t find the definition, so it’s very possible that I just missed it.

⭐This book has been very challenging for me. I’m not a mathematician (except in my dreams), and this book is heavy with abstract theory. One of the biggest challenges is that the book uses symbology not familiar to me, and there is no glossary of symbols (which would be VERY useful).I would be interested in what others with a more mathematical background think about the book — am I wasting my time trying to slog through it?For someone just trying to get a feel for nonlinear dynamics and chaos, I strongly recommend Steven Strogatz’s book “Nonlinear Dynamics And Chaos”.

⭐Es el libro que te aconsejan en la Universidad de Matematicas, es segundo de carrera.Un buen aliado para entender ciertos conceptos.

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