Jager T.H. The creation of strange non-chaotic attractors in non-smooth saddle-node bifurcations. - Providence: American Mathematical Society, 2009. - vi, 106 p.: ill. - (Memoirs of the American Mathematical Society; Vol.201, N 945 (fourth of 5 numbers)). - Bibliogr.: p.105-106. - ISBN 978-0-8218-4427-4; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

Chapter 1 ntroduction .......................................... 1 1.1 Overview ................................................... 3 1.2 Basic definitions and notations ............................ 5 1.3 Examples of non-smooth saddle-node bifurcations ............ 6 1.4 The mechanism: Exponential evolution of peaks ............. 15 Chapter 2 Statement of the main results and applications ...... 21 2.1 A general setting for saddle-node bifurcations in qpf interval maps ............................................. 21 2.2 Sink-source-orbits and the existence of SNA ............... 23 2.3 Non-smooth bifurcations ................................... 26 2.4 Application to the parameter families ..................... 29 Chapter 3 Saddle-node bifurcations and sink-source-orbits ..... 36 3.1 Equivalence classes of invariant graphs and the essential closure ......................................... 36 3.2 Saddle-node bifurcations: Proof of Theorem 2.1 ............ 37 3.3 Sink-source-orbits and SNA: Proof of Theorem 2.4 .......... 42 Chapter 4 The strategy for the construction of the sink- source-orbits ....................................... 44 4.1 The first stage of the construction ....................... 44 4.2 Dealing with the first close return ....................... 46 4.3 Admissible and regular times .............................. 50 4.4 Outline of the further strategy ........................... 51 Chapter 5 Tools for the construction .......................... 54 5.1 Comparing orbits .......................................... 54 5.2 Approximating sets ........................................ 59 5.3 Exceptional intervals and admissible times ................ 62 5.4 Regular times ............................................. 68 Chapter 6 Construction of the sink-source orbits: One-sided forcing ............................................. 73 6.1 Proof of the induction scheme ............................. 77 Chapter 7 Construction of the sink-source-orbits: Symmetric forcing ............................................. 92 7.1 Proof of the induction scheme ............................. 95 Bibliography .................................................. 105