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Dynamics of Topologically Generic Homeomorphisms.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2003Copyright date: ©2003Edition: 1st edDescription: 1 online resource (146 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470403812
Subject(s): Genre/Form: Additional physical formats: Print version:: Dynamics of Topologically Generic HomeomorphismsDDC classification:
  • 510 s;514
LOC classification:
  • QA613.7 -- .A35 2003eb
Online resources:
Contents:
Intro -- Contents -- Introduction -- 0.1. Overview -- 0.2. Description of results -- 0.3. Brief remarks about techniques -- 0.4. Comparison with the smooth case -- 0.5. Standing notation -- 0.6. Road map -- 0.7. Comments -- Chapter 1. Attractors and Chain Recurrence -- 1.1. Chain recurrence -- 1.2. Attractors -- 1.3. Attractor-repellor pairs -- 1.4. Initial and terminal chain components -- 1.5. The space(s) of chain components -- 1.6. Summary -- Chapter 2. Periodic Decompositions and Adding Machines -- 2.1. Periodic decompositions -- 2.2. The sets II∞ and II[sub(∞,&amp -- #8734)] -- -- 2.3. Adding machines -- 2.4. Decompositions of U type -- 2.5. Periodicity conditions -- Chapter 3. Semicontinuity and Homogeneity -- 3.1. Semicontinuity -- 3.2. Prolongation -- 3.3. The automorphism group -- 3.4. Homogeneity conditions -- 3.5. Showing Ω(f) = C(f) -- Chapter 4. Crushing Arguments -- 4.1. Sponges -- 4.2. Crushing -- Chapter 5. Topological Horseshoes -- 5.1. Connected successions of subsets -- 5.2. Topological horseshoes -- 5.3. Perturbing to a horseshoe -- Chapter 6. Generic Homeomorphisms -- 6.1. The classes H[sub(s)] and H[sub(1,s)] -- 6.2. The class H[sub(3,s)] -- 6.3. Dynamic isolation -- 6.4. Attractor boundaries are quasi- attractors -- 6.5. Shift extensions and the class H[sub(4)] -- Chapter 7. Almost Equicontinuity -- 7.1. Chain continuity -- Chapter 8. Cantor Sets -- 8.1. Aperiodicity and the class H[sub(5)] -- 8.2. The class H[sub(6)] -- 8.3. Rohlin property -- 8.4. The class H[sub(3,s)] -- Chapter 9. The Circle -- 9.1. Background -- 9.2. The class H[sub(1)] on S[sup(1)] -- 9.3. Relative Rohlin property -- Chapter 10. Crushing the Chain Recurrent Set -- Chapter 11. Generic Homeomorphisms on Manifolds -- 11.1. The class H[sub(8)] -- 11.2. The class H[sub(man )] -- 11.3. Anosov homeomorphisms -- Chapter 12. Generic Mappings on Manifolds.
Bibliography -- Index.
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Intro -- Contents -- Introduction -- 0.1. Overview -- 0.2. Description of results -- 0.3. Brief remarks about techniques -- 0.4. Comparison with the smooth case -- 0.5. Standing notation -- 0.6. Road map -- 0.7. Comments -- Chapter 1. Attractors and Chain Recurrence -- 1.1. Chain recurrence -- 1.2. Attractors -- 1.3. Attractor-repellor pairs -- 1.4. Initial and terminal chain components -- 1.5. The space(s) of chain components -- 1.6. Summary -- Chapter 2. Periodic Decompositions and Adding Machines -- 2.1. Periodic decompositions -- 2.2. The sets II∞ and II[sub(∞,&amp -- #8734)] -- -- 2.3. Adding machines -- 2.4. Decompositions of U type -- 2.5. Periodicity conditions -- Chapter 3. Semicontinuity and Homogeneity -- 3.1. Semicontinuity -- 3.2. Prolongation -- 3.3. The automorphism group -- 3.4. Homogeneity conditions -- 3.5. Showing Ω(f) = C(f) -- Chapter 4. Crushing Arguments -- 4.1. Sponges -- 4.2. Crushing -- Chapter 5. Topological Horseshoes -- 5.1. Connected successions of subsets -- 5.2. Topological horseshoes -- 5.3. Perturbing to a horseshoe -- Chapter 6. Generic Homeomorphisms -- 6.1. The classes H[sub(s)] and H[sub(1,s)] -- 6.2. The class H[sub(3,s)] -- 6.3. Dynamic isolation -- 6.4. Attractor boundaries are quasi- attractors -- 6.5. Shift extensions and the class H[sub(4)] -- Chapter 7. Almost Equicontinuity -- 7.1. Chain continuity -- Chapter 8. Cantor Sets -- 8.1. Aperiodicity and the class H[sub(5)] -- 8.2. The class H[sub(6)] -- 8.3. Rohlin property -- 8.4. The class H[sub(3,s)] -- Chapter 9. The Circle -- 9.1. Background -- 9.2. The class H[sub(1)] on S[sup(1)] -- 9.3. Relative Rohlin property -- Chapter 10. Crushing the Chain Recurrent Set -- Chapter 11. Generic Homeomorphisms on Manifolds -- 11.1. The class H[sub(8)] -- 11.2. The class H[sub(man )] -- 11.3. Anosov homeomorphisms -- Chapter 12. Generic Mappings on Manifolds.

Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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