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El. knyga: Introduction To Nonlinear Dynamics For Physicists

(Univ Of California, Usa), (Therma-wave, Inc., Usa), (Univ Of California, San Diego, Usa)
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This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.
Nonlinear oscillator without dissipation; equilibrium states of a
nonlinear oscillator with dissipation; oscillations in systems with nonlinear
dissipation-generators; the Van der Pol generator; the Poincare map; slow and
fast motions in systems with one degree of freedom; forced nonlinear
oscillators; linear and nonlinear resonances; forced generator -
synchronization; competition of modes; Poincare indices and bifurcations of
equilibrium states; resonance interactions between oscillators; solitons;
steady propagation of shock waves; formation of shock waves; solitons; shock
waves; wave interaction; the spectral approach; weak turbulance; random phase
approximation; regular patterns in dissipative media; deterministic chaos;
qualitative description; description of a circuit with chaos; chaos in maps;
bifurcations of periodic motions; period doubling; controlled nonlinear
oscillator; ways to chaos; intermittency; scenarios of the onset of chaos;
chaos through quasi-periodicity; characteristics of chaos; experimental
observation of chaos; multidimensional chaos; discrete Ginzburg-Landau model.
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