Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics

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November 2005



A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.


Preface; 1. Hyperbolicity, stability and sensitive-chaotic dynamical systems; 2. Examples of homoclinic orbits in dynamical systems; 3. Dynamical consequences of a transverse homoclinic intersection; 4. Homoclinic tangencies: cascades of bifurcations, scaling and quadratic maps; 5. Cantor sets in dynamics and fractal dimensions; 6. Homoclinic bifurcations: fractal dimensions and measure of bifurcation sets; 7. Infinitely many sinks and homoclinic tangencies; 8. Overview, conjectures and problems - a theory of homoclinic bifurcations - strange attractors; Appendices; References.


" interesting monograph on this collection of ideas. It begins with material often covered in graduate texts but quickly moves to the exposition of ideas only available in the original sources. It would be quite suitable for an advanced graduate level course in dynamics and bifurcation theory." John Franks, Bulletin of the American Mathematical Society
EAN: 9780521475723
ISBN: 0521475724
Untertitel: 'Cambridge Studies in Advanced'. Revised. Sprache: Englisch.
Erscheinungsdatum: November 2005
Seitenanzahl: 248 Seiten
Format: kartoniert
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