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Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2009Copyright date: ©2009Edition: 1st edDescription: 1 online resource (120 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470405595
Subject(s): Genre/Form: Additional physical formats: Print version:: Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node BifurcationsDDC classification:
  • 515/.39
LOC classification:
  • QA614.813 -- .J34 2009eb
Online resources:
Contents:
Intro -- Contents -- Chapter 1. Introduction -- 1.1. Overview -- 1.2. Basic definitions and notations -- 1.3. Examples of non-smooth saddle-node bifurcations -- 1.4. The mechanism: Exponential evolution of peaks -- Chapter 2. Statement of the main results and applications -- 2.1. A general setting for saddle-node bifurcations in qpf interval maps -- 2.2. Sink-source-orbits and the existence of SNA -- 2.3. Non-smooth bifurcations -- 2.4. Application to the parameter families -- Chapter 3. Saddle-node bifurcations and sink-source-orbits -- 3.1. Equivalence classes of invariant graphs and the essential closure -- 3.2. Saddle-node bifurcations: Proof of Theorem 2.1 -- 3.3. Sink-source-orbits and SNA: Proof of Theorem 2.4 -- Chapter 4. The strategy for the construction of the sink-source-orbits -- 4.1. The first stage of the construction -- 4.2. Dealing with the first close return -- 4.3. Admissible and regular times -- 4.4. Outline of the further strategy -- Chapter 5. Tools for the construction -- 5.1. Comparing orbits -- 5.2. Approximating sets -- 5.3. Exceptional intervals and admissible times -- 5.4. Regular times -- Chapter 6. Construction of the sink-source orbits: One-sided forcing -- 6.1. Proof of the induction scheme -- Chapter 7. Construction of the sink-source-orbits: Symmetric forcing -- 7.1. Proof of the induction scheme -- Bibliography.
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Intro -- Contents -- Chapter 1. Introduction -- 1.1. Overview -- 1.2. Basic definitions and notations -- 1.3. Examples of non-smooth saddle-node bifurcations -- 1.4. The mechanism: Exponential evolution of peaks -- Chapter 2. Statement of the main results and applications -- 2.1. A general setting for saddle-node bifurcations in qpf interval maps -- 2.2. Sink-source-orbits and the existence of SNA -- 2.3. Non-smooth bifurcations -- 2.4. Application to the parameter families -- Chapter 3. Saddle-node bifurcations and sink-source-orbits -- 3.1. Equivalence classes of invariant graphs and the essential closure -- 3.2. Saddle-node bifurcations: Proof of Theorem 2.1 -- 3.3. Sink-source-orbits and SNA: Proof of Theorem 2.4 -- Chapter 4. The strategy for the construction of the sink-source-orbits -- 4.1. The first stage of the construction -- 4.2. Dealing with the first close return -- 4.3. Admissible and regular times -- 4.4. Outline of the further strategy -- Chapter 5. Tools for the construction -- 5.1. Comparing orbits -- 5.2. Approximating sets -- 5.3. Exceptional intervals and admissible times -- 5.4. Regular times -- Chapter 6. Construction of the sink-source orbits: One-sided forcing -- 6.1. Proof of the induction scheme -- Chapter 7. Construction of the sink-source-orbits: Symmetric forcing -- 7.1. Proof of the induction scheme -- Bibliography.

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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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