Chaos Near Resonance : Applied Mathematical Sciences, 138 - G. Haller

Chaos Near Resonance

By: G. Haller

Hardcover | 1 October 1999

At a Glance

Hardcover


$101.07

or 4 interest-free payments of $25.27 with

 or 

Aims to ship in 7 to 10 business days

When will this arrive by?
Enter delivery postcode to estimate

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 Previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds are described.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.
Industry Reviews
"An extensive bibliography and the many examples make this clearly-written book an excellent introduction to these techniques for identifying chaos in perturbations of systems with resonance."
Applied Mechanics Reviews, Vol. 53/4, April 2000

"Haller makes a point of wanting to see dynamical systems theory fulfil "its long-standing promise to solve real-life problems". His book, through a wealth of detailed examples, delivers on this promise, and is certain ti become a standard text in this area. In particular, it is an excellent introduction to this research area, and contains a wealth of bibliographical and historical detail.
Matthew Nicol, Bulletin of the LMS, No. 162, Vol. 33/3, May 2001

More in Mathematics

Nelson WAmaths Mathematics Applications : 11th Edition - Amanda Pettitt
How to Win At Chess : The Ultimate Guide for Beginners and Beyond - Levy Rozman
Nelson WAmaths Mathematics Methods : 11th Edition - Judith Cumpsty
Calculus, Metric Edition : 9th edition - James Michael Stewart

RRP $174.95

$141.75

19%
OFF
The Selfish Gene : 40th Anniversary Edition - Richard Dawkins
Discovering Statistics Using IBM SPSS Statistics : (Paperback plus Ebook) 5ed - Andy Field
Aristotle's Organon in Old and New Logic : 1800-1950 - Colin Guthrie  King

RRP $170.00

$125.75

26%
OFF
Antifragile : Things That Gain from Disorder - Nassim Nicholas Taleb
Basic Technical Mathematics with Calculus, SI Version : 11th edition - Allyn J. Washington
Fuzzy Methods for Assessment and Decision Making - Michael Gr. Voskoglou

RRP $264.95

$199.95

25%
OFF