Topological classification of families of diffeomorphisms without small divisors / Javier Ribón.

Format:

Book

Author/Creator:

Ribón, Javier, 1974- author.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.207

Language:

English

Subjects (All):

Topological dynamics.

Diffeomorphisms.

Differentiable dynamical systems.

Physical Description:

1 online resource (166 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Psychological Association, 2010.

Language Note:

English

Summary:

The author gives a complete topological classification for germs of one-parameter families of one-dimensional complex analytic diffeomorphisms without small divisors. In the non-trivial cases the topological invariants are given by some functions attached to the fixed points set plus the analytic class of the element of the family corresponding to the special parameter. The proof is based on the structure of the limits of orbits when we approach the special parameter.

Contents:

""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""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0589-X