Ribón J. Topological classification of families of diffeomorphisms without small divisors. - Providence: American Mathematical Society, 2010. - ix, 166 p. - (Memoirs of the American Mathematical Society; Vol.207, N 975). - Bibliogr.: p.163. - Ind.: p.165-166. - ISBN 978-0-8218-4748-0; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ....................................................... vii Chapter 1 Outline of the Monograph ............................. 1 Chapter 2 Flower Type Vector Fields ........................... 11 2.1 Definition and basic properties ........................... 11 2.2 Families of vector fields without small divisors .......... 23 Chapter 3 A Clockwork Orange .................................. 27 3.1 Exterior dynamics ......................................... 27 3.2 The magnifying glass ...................................... 43 Chapter 4 The T-sets .......................................... 49 4.1 Unstable set and bi-tangent cords ......................... 49 4.2 Dynamical instability ..................................... 57 4.3 Disassembling the graph ................................... 60 Chapter 5 The Long Limits ..................................... 65 5.1 Setup and non-oscillation properties ...................... 66 5.2 Definition of the Long Limits ............................. 68 5.3 Structure of the Long Limits .............................. 70 5.4 Evolution of the Long Limits .............................. 73 Chapter 6 Topological Conjugation of (NSD) Vector Fields ...... 79 6.1 Orientation ............................................... 80 6.2 Comparing residues ........................................ 81 6.3 Topological invariants .................................... 87 Chapter 7 Families of Diffeomorphisms without Small Divisors ............................................ 97 7.1 Normal form and residues .................................. 98 7.2 Comparing a diffeomorphism and its normal form ........... 100 7.3 Long orbits .............................................. 107 Chapter 8 Topological Invariants of (NSD) Diffeomorphisms .... 111 8.1 Topological invariants ................................... 111 8.2 Theorem of topological conjugation ....................... 116 Chapter 9 Tangential Conjugations ............................ 123 9.1 Plan of the chapter ...................................... 124 9.2 Preparation of φ1 and φ2 ................................. 124 9.3 Shaping the domains ...................................... 126 9.4 Base transversals ........................................ 131 9.5 The M-interpolation process .............................. 135 9.6 Regions and their limiting curves ........................ 139 9.7 Conjugating a diffeomorphism and its normal form ......... 145 9.8 Comparing tg-conjugations ................................ 148 List of Notations ............................................. 161 Bibliography .................................................. 163 Index ......................................................... 165