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| Author | : Jacob Palis Júnior |
| Publisher | : Cambridge University Press |
| Total Pages | : 248 |
| Release | : 1995-01-05 |
| Genre | : Mathematics |
| ISBN | : 9780521475723 |
A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
| Author | : Jacob Palis Júnior |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1993 |
| Genre | : Bifurcation theory |
| ISBN | : |
| Author | : Paul Glendinning |
| Publisher | : Cambridge University Press |
| Total Pages | : 404 |
| Release | : 1994-11-25 |
| Genre | : Mathematics |
| ISBN | : 1316583570 |
By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.
| Author | : Paul Glendinning |
| Publisher | : Cambridge University Press |
| Total Pages | : 408 |
| Release | : 1994-11-25 |
| Genre | : Mathematics |
| ISBN | : 9780521425667 |
An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
| Author | : Stephen Wiggins |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 505 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 1461210429 |
Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.
| Author | : Jacob Palis Júnior |
| Publisher | : |
| Total Pages | : 148 |
| Release | : 1987 |
| Genre | : Bifuraction theory |
| ISBN | : |
Dynamic consequences of a transverse homoclinic intersection. Homoclinic tangencies: Cascade of bifurcations, sacaling and quadratic maps. Cantor sets. Homoclinic tangencies, cantor sets, measure of bifurcation sets. Infinitely many sinks. Hyperbolicity. Markov partitions. Heteroclinic cycles. On the shape of some strange attractors.
| Author | : Guangxuan Li |
| Publisher | : |
| Total Pages | : 508 |
| Release | : 1987 |
| Genre | : Bifurcation theory |
| ISBN | : |
| Author | : Jacob Palis Júnior |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1993 |
| Genre | : Bifurcation theory |
| ISBN | : |
| Author | : David Ruelle |
| Publisher | : Elsevier |
| Total Pages | : 196 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483272184 |
Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
| Author | : Yushu Chen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 465 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1447115759 |
For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.
