Topological Classification of Families of Diffeomorphisms without Small Divisors.
- 1st ed.
- 1 online resource (183 pages)
- Memoirs of the American Mathematical Society ; v.207 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- Preface -- Chapter 1. Outline of the Monograph -- Chapter 2. Flower Type Vector Fields -- 2.1. Definition and basic properties -- 2.2. Families of vector fields without small divisors -- Chapter 3. A Clockwork Orange -- 3.1. Exterior dynamics -- 3.2. The magnifying glass -- Chapter 4. The T-sets -- 4.1. Unstable set and bi-tangent cords -- 4.2. Dynamical instability -- 4.3. Disassembling the graph -- Chapter 5. The Long Limits -- 5.1. Setup and non-oscillation properties -- 5.2. Definition of the Long Limits -- 5.3. Structure of the Long Limits -- 5.4. Evolution of the Long Limits -- Chapter 6. Topological Conjugation of (NSD) Vector Fields -- 6.1. Orientation -- 6.2. Comparing residues -- 6.3. Topological invariants -- Chapter 7. Families of Diffeomorphisms without Small Divisors -- 7.1. Normal form and residues -- 7.2. Comparing a diffeomorphism and its normal form -- 7.3. Long orbits -- Chapter 8. Topological Invariants of (NSD) Diffeomorphisms -- 8.1. Topological invariants -- 8.2. Theorem of topological conjugation -- Chapter 9. Tangential Conjugations -- 9.1. Plan of the chapter -- 9.2. Preparation of 1 and 2 -- 9.3. Shaping the domains -- 9.4. Base transversals -- 9.5. The M-interpolation process -- 9.6. Regions and their limiting curves -- 9.7. Conjugating a diffeomorphism and its normal form -- 9.8. Comparing tg-conjugations -- List of Notations -- Bibliography -- Index.