{"product_id":"stable-and-random-motions-in-dynamical-systems-9780691089102","title":"Stable and Random Motions in Dynamical Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents an account of two pillars of the techniques of nonlinear dynamics and chaos theory: stable and chaotic behavior. This title discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeward ix  I. INTRODUCTION 3  1. The stability problem 3  2. Historical comments 3  3. Other problems 8  4. Unstable and statistical behavior 14  5. Plan 18  II. STABILITY PROBLEM 21  1. A model problem in the complex 21  2. Normal forms for Hamiltonian and reversible systems 30  3. Invariant manifolds 38  4. Twist theorem 50  III. STATISTICAL BEHAVIOR 61  1. Bernoulli shift. Example 61  2. Shift as a topological mapping 66  3. Shift as a subsystem 68  4. Alternate conditions for C'-mappings 76  5. The restricted three-body problem 83  6. Homoclinic points 99  IV. FINAL REMARKS 113  V. EXISTENCE PROOF IN THE PRESENCE OF SMALL DIVISORS 113  1. Reformulation of Theorem 2.9 113  2. Construction of the root of a function 120  3. Proof of Theorem 5.1 127  4. Generalities 138  A. Appendix to Chapter V 149  a. Rate of convergence for scheme of s.2b) 149  b. The improved scheme by Hald 151  VI. PROOFS AND DETAILS FOR CHAPTER III 153  1. Outline 153  2. Behavior near infinity 154  3. Proof of Lemmas 1 and 2 of Chapter III 160  4. Proof of Lemma 3 of Chapter III 163  5. Proof of Lemma 4 of Chapter III 167  6. Proof of Lemma 5 of Chapter III 171  7. Proof of Theorem 3.7, concerning homoclinic points 181  8. Nonexistence of intergals 188  BOOKS AND SURVEY ARTICLES 191","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49526153838935,"sku":"9780691089102","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691089102.jpg?v=1731863152","url":"https:\/\/bookcurl.com\/products\/stable-and-random-motions-in-dynamical-systems-9780691089102","provider":"Book Curl","version":"1.0","type":"link"}