Nonlinear dynamics: A two-way trip from physics to math
- New Delhi, Overseas Press India Private Limited: 2005.
- xviii, 347p. : ill.
Bibliographical references 335-342p.; Index 343-347p.
Acknowledgments Preface Nonlinear dynamics in nature - Hiking among rabbits, Turbulence, Benard instability, Dynamics of a modulated laser, Tearing of plasma sheet, Summary Linear dynamics - Introduction, Why linear dynamics?, Linear flows, Summary, Additional exercise Nonlinear examples - Preliminary comments, A model for the CO2 Laser, Duffering oscillator, The Lorenz equations, Summary, Additional exercises Elements of the description - Introduction, Basic elements, Poincare sections, Maps and dynamics, Parameter dependence, Summary, Additional exercise Elementary stability theory - Introduction, Fixed point stability, The validity of the linearization procedure, Maps and periodic orbits, Structural stability, Summary, Additional exercise Bi-dimensional flows - Limit sets, Transverse sections and sequences, Poincare - Bendixson theorem, Structural Stability, Summary Bifurcations - The bifurcation programme, Equivalence between flows, Conditions for fixed point bifurcations, Reduction to the centre manifold, Normal forms, Additional exercise Numerical experiments - Period-doubling cascades, Torus break up, Homoclinic explosions in the Lorenz systems, chaos and other phenomena, Summary Global bifurcations - Transverse homoclinic orbits, Homoclinic tangencies, Homoclinic tangles and horseshoes, Heteroclinic tangles, SummaryHorseshoes - The invariant set, Cantor sets, Symbolic dynamics, Horseshoes and attractors, Hyperbolicity, Structural stability, Summary, Addtional exercise One-dimensional Maps - Unimodal maps of the interval, Elementary kneading theory, Parametric families of unimodal maps, Summary Topological structure of three-dimensional flows - Introduction, Forced oscillators and two dimensional maps, Topological invariants, Orbits that imply chaos, Horseshoe formation, Topological classification of strange attractors, Summary The dynamics behind data - Introduction and motivation, Characterization of chaotic time series, Is this data set chaotic?, , Summar