Chapter 1 Principal structures

Publisher Summary Dynamical systems have grown from various roots into a field of great diversity that interacts with many branches of mathematics as well as with the sciences. This chapter presents a survey to describe the general framework for several principal areas of the theory of dynamical systems. A possible use of this survey is as an introduction to mathematicians unfamiliar with dynamics, and it may be interesting to experts as an overview of a diverse field. The chapter focuses on examples, motivations, informal explanations, and discussion of key special cases or simplified versions of general results of dynamical systems. The chapter introduces a collection of important notions in generic terms—that is, without relying on any specific structure of the dynamical system. It introduces basic examples and intersperse further examples, as well as comments on previously introduced ones. The central structural elements are presented in the chapter in the order: the notions of equivalence, principal constructions, recurrence, and orbit growth.

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