000			02125nam a22002057a 4500
003			OSt
005			20240828121448.0
008			190117b ||||| |||| 00| 0 eng d
020			_a0387908196
040			_cTata Book House _aICTS-TIFR
050			_aQA1
100			_aGuckenheimer, John
245			_a Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
260			_aNew York: _bSpringer Verlag, _c[c1983]
300			_a459 p.
505			_a1. Introduction: Differential Equations and Dynamical Systems 2. An Introduction to Chaos: Four Examples 3. Local Bifurcations 4. Averaging and Perturbation from a Geometric Viewpoint 5. Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors 6. Global Bifurcations 7. Local Codimension Two Bifurcations of Flows
520			_aThis book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations
700			_aHolmes, Philip
942			_2lcc _cBK
999			_c2138 _d2138