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Chaos Near Resonance (Hardcover, 1999 ed.)
Loot Price: R1,838
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Chaos Near Resonance (Hardcover, 1999 ed.)
Series: Applied Mathematical Sciences, 138
Expected to ship within 10 - 15 working days
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Resonances are ubiquitous in dynamical systems with many degrees of
freedom. They have the basic effect of introducing slow-fast
behavior in an evolutionary system which, coupled with
instabilities, can result in highly irregular behavior. This book
gives a unified treatment of resonant problems with special
emphasis on the recently discovered phenomenon of homoclinic
jumping. After a survey of the necessary background, a general
finite dimensional theory of homoclinic jumping is developed and
illustrated with examples. The main mechanism of chaos near
resonances is discussed in both the dissipative and the Hamiltonian
context. Previously unpublished new results on universal homoclinic
bifurcations near resonances, as well as on multi-pulse Silnikov
manifolds are described. The results are applied to a variety of
different problems, which include applications from beam
oscillations, surface wave dynamics, nonlinear optics, atmospheric
science and fluid mechanics. The theory is further used to study
resonances in Hamiltonian systems with applications to molecular
dynamics and rigid body motion. The final chapter contains an
infinite dimensional extension of the finite dimensional theory,
with application to the perturbed nonlinear Schrodinger equation
and coupled NLS equations."
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