Abstract
In this chapter we will discuss some problems of dynamics and chaos in nonstandard Hamiltonian systems. First of these problems is the dynamics of Hamiltonian systems in which a so-called twist condition is violated. Particular example of these system is a one–degree-of-freedom system with a non-monotonic dependence of the frequency of oscillations on action variable. The second problem is a study of systems subjected to non-smooth perturbations. These problems have been mainly investigated in the last decade, and they are less discussed in monographes and reviews. Regular and chaotic dynamics of these Hamiltonian systems are outside the scope of the Kolmogorov–Arnold–Moser (KAM) theory. Before discussing these problems we recall the KAM theory and the onset of chaotic dynamics in standard Hamiltonian systems. We will use the mapping approach to study these problems.
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© 2006 Springer
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Abdullaev, S.S. (2006). The KAM Theory Chaos Nontwist and Nonsmooth Maps. In: Construction of Mappings for Hamiltonian Systems and Their Applications. Lecture Notes in Physics, vol 691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33417-3_7
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DOI: https://doi.org/10.1007/3-540-33417-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30915-4
Online ISBN: 978-3-540-33417-0
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