[PDF] Lectures In Differentiable Dynamics eBook

Author : Lawrence Markus
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 11,53 MB
Release : 1980
Category : Mathematics
ISBN : 0821816950

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Offers an exposition of the central results of Differentiable Dynamics. This edition includes an Appendix reviewing the developments under five basic areas: nonlinear oscillations, diffeomorphisms and foliations, general theory; dissipative dynamics, general theory; conservative dynamics, and, chaos, catastrophe, and multi-valued trajectories.

Author : Lan Wen
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 44,58 MB
Release : 2016-07-20
Category : Mathematics
ISBN : 1470427990

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This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 30,72 MB
Release : 2018-05-04
Category : Mathematics
ISBN : 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Author : Kotik K. Lee
Publisher : World Scientific
Page : 476 pages
File Size : 39,21 MB
Release : 1992
Category : Science
ISBN : 9789971509651

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The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.