Introduction to the modern theory of dynamical systems /
This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in...
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| Format: | Book |
| Language: | English |
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Cambridge ; New York, NY, USA :
Cambridge University Press,
1995.
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| Series: | Encyclopedia of mathematics and its applications ;
v. 54. |
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Table of Contents:
- pt. 1. Examples and fundamental concepts. 1. First examples. 1. Maps with stable asymptotic behavior. 2. Linear maps. 3. Rotations of the circle. 4. Translations on the torus. 5. Linear flow on the torus and completely integrable systems. 6. Gradient flows. 7. Expanding maps. 8. Hyperbolic toral automorphisms. 9. Symbolic dynamical systems. 2. Equivalence, classification, and invariants. 1. Smooth conjugacy and moduli for maps. 2. Smooth conjugacy and time change for flows. 3. Topological conjugacy, factors, and structural stability. 4. Topological classification of expanding maps on a circle. 5. Coding, horseshoes, and Markov partitions. 6. Stability of hyperbolic toral automorphisms. 7. The fast-converging iteration method (Newton method) for the conjugacy problem. 8. The Poincare-Siegel Theorem. 9. Cocycles and cohomological equations. 3. Principal classes of asymptotic topological invariants. 1. Growth of orbits. 2. Examples of calculation of topological entropy.