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" Nonlinear dynamics : "


Document Type : BL
Record Number : 874432
Main Entry : Solari, H. G., (Hernán G.)
Title & Author : Nonlinear dynamics : : a two-way trip from physics to math /\ H.G. Solari, M.A. Natiello, G.B. Mindlin.
Publication Statement : Bristol ;Philadelphia :: Institute of Physics Pub.,, ©1996.
Page. NO : 1 online resource (369 pages) :: illustrations
ISBN : 0203745612
: : 1351428306
: : 9780203745618
: : 9781351428309
: 1138458163
: 9780750303804
: 9781138458161
Notes : 7.6 Simplest local bifurcations of fixed points
Bibliographies/Indexes : Includes bibliographical references and index.
Contents : Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Acknowledgments; Preface; 1: Nonlinear dynamics in nature; 1.1 Hiking among rabbits; 1.2 Turbulence; 1.3 Bénard instability; 1.4 Dynamics of a modulated laser; 1.5 Tearing of a plasma sheet; 1.6 Summary; 2: Linear dynamics; 2.1 Introduction; 2.2 Why linear dynamics?; 2.3 Linear flows; 2.3.1 Autonomous flows; 2.3.1.1 Autonomous homogeneous flows; 2.3.1.2 Autonomous inhomogeneous flows; 2.3.1.3 Singular points in bi-dimensional flows; 2.3.2 Forced flows; 2.3.2.1 Additively forced flows
: 2.3.2.2 Parametrically forced flows2.3.2.3 Floquet's theorem; 2.3.2.4 Oscillation theorem-Liapunov-Haupt; 2.3.2.5 Arnold tongues; 2.4 Summary; 2.5 Additional exercise; 3: Nonlinear examples; 3.1 Preliminary comments; 3.2 A model for the CO2 laser; 3.2.1 The model; 3.2.2 Dynamics of the laser; 3.3 Duffing oscillator; 3.3.1 The model; 3.3.2 Dynamics in the unforced model; 3.4 The Lorenz equations; 3.4.1 The model; 3.4.1.1 Properties; 3.4.2 Simple dynamics in the Lorenz model; 3.5 Summary; 3.6 Additional exercises; 4: Elements of the description; 4.1 Introduction; 4.2 Basic elements
: 4.2.1 Phase space4.2.2 Flow; 4.2.3 Invariants; 4.2.3.1 Orbits; 4.2.4 Attractors; 4.2.4.1 Attracting sets; 4.2.4.2 Attractors; 4.2.4.3 Basin of attraction; 4.2.4.4 Boundaries of the basin of attraction; 4.2.5 Trapping regions; 4.2.6 Stable and unstable sets; 4.3 Poincaré sections; 4.3.1 Stroboscopic section; 4.3.2 Transverse section; 4.3.3 Poincaré sections and Poincaré first-return maps; 4.3.3.1 Global Poincaré section; 4.3.3.2 Local Poincaré section; 4.4 Maps and dynamics; 4.4.1 Properties of maps; 4.4.1.1 Conjugated maps; 4.5 Parameter dependence; 4.5.1 Families of flows and maps
: 4.6 Summary4.7 Additional exercise; 5: Elementary stability theory; 5.1 Introduction; 5.2 Fixed point stability; 5.2.1 Liapunov stability criteria; 5.3 The validity of the linearization procedure; 5.4 Maps and periodic orbits; 5.4.1 Maps; 5.4.2 Periodic orbits of flows, Floquet stability theory; 5.5 Structural stability; 5.5.1 Orbital equivalence; 5.5.2 Structural equivalence; 5.6 Summary; 5.7 Additional exercise; 6: Bi-dimensional flows; 6.1 Limit sets; 6.2 Transverse sections and sequences; 6.3 Poincaré-Bendixson theorem; 6.4 Structural stability; 6.5 Summary; 7: Bifurcations
: 7.1 The bifurcation programme7.1.1 Families of flows and maps; 7.1.2 Local and global bifurcations; 7.1.3 Local bifurcations: the programme; 7.2 Equivalence between flows; 7.3 Conditions for fixed point bifurcations; 7.3.1 Unfolding of a bifurcation; 7.4 Reduction to the centre manifold; 7.4.1 Adiabatic elimination of fast-decaying variables; 7.4.2 Approximation to the centre manifold; 7.4.3 Centre manifold for maps; 7.4.4 Bifurcations; 7.5 Normal forms; 7.5.1 Example: Jordan block; 7.5.2 The general case; 7.5.3 Normal forms for maps; 7.5.4 Resonances; 7.5.4.1 Small denominators
Subject : Dynamics.
Subject : Mathematical physics.
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