Fixed Point Theorems for Plane Continua with Applications.
- 1st ed.
- 1 online resource (117 pages)
- Memoirs of the American Mathematical Society ; v.224 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- List of Figures -- Preface -- Chapter 1. Introduction -- Part 1 . Basic Theory -- Chapter 2. Preliminaries and outline of Part 1 -- 2.1. Index -- 2.2. Variation -- 2.3. Classes of maps -- 2.4. Partitioning domains -- Chapter 3. Tools -- 3.1. Stability of Index -- 3.2. Index and variation for finite partitions -- 3.3. Locating arcs of negative variation -- 3.4. Crosscuts and bumping arcs -- 3.5. Index and Variation for Carathéodory Loops -- 3.6. Prime Ends -- 3.7. Oriented maps -- 3.8. Induced maps of prime ends -- Chapter 4. Partitions of domains in the sphere -- 4.1. Kulkarni-Pinkall Partitions -- 4.2. Hyperbolic foliation of simply connected domains -- 4.3. Schoenflies Theorem -- 4.4. Prime ends -- Part 2 . Applications of Basic Theory -- Chapter 5. Description of main results of Part 2 -- 5.1. Outchannels -- 5.2. Fixed points in invariant continua -- 5.3. Fixed points in non-invariant continua -the case of dendrites -- 5.4. Fixed points in non-invariant continua -the planar case -- 5.5. The polynomial case -- Chapter 6. Outchannels and their properties -- 6.1. Outchannels -- 6.2. Uniqueness of the Outchannel -- Chapter 7. Fixed points -- 7.1. Fixed points in invariant continua -- 7.2. Dendrites -- 7.3. Non-invariant continua and positively oriented maps of the plane -- 7.4. Maps with isolated fixed points -- 7.5. Applications to complex dynamics -- Bibliography -- Index.