Differentiable Dynamical Systems

An Introduction to Structural Stability and Hyperbolicity

LAN Wen (Autor)

Buch | Hardcover

192 Seiten

2016
American Mathematical Society (Verlag)
978-1-4704-2799-3 (ISBN)

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This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale.

While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study.

Lan Wen, Peking University, Beijing, China.

Basics of dynamical systems
Hyperbolic fixed points
Horseshoes, toral automorphisms, and solenoids
Hyperbolic sets
Axiom A, no-cycle condition, and Ω-stability
Quasi-hyperbolicity and linear transversality
Bibliography
Index

Erscheinungsdatum	17.08.2016
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	526 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2799-0 / 1470427990
ISBN-13	978-1-4704-2799-3 / 9781470427993
Zustand	Neuware