Abstract
Poincaré (1892–99) introduced a powerful tool to study dynamical systems by replacing continuous systems by discrete mappings. As was mentioned in the preface mappings significantly simplify the study of systems, by reducing the dimension of the system by one, visualizing the orbits on certain sections of phase space, and thus simplifying the formulation of many concepts of dynamical systems. In this chapter we review the traditional methods to construct symplectic maps for generic continuous Hamiltonian systems. We consider the generic Hamiltonian system (2.2) with small time-periodic perturbations. We shall discuss the main difficulties to construct mappings from Hamiltonian equations, and the shortcomings.
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© 2006 Springer
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Abdullaev, S.S. (2006). Mappings for Perturbed Systems. 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_3
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DOI: https://doi.org/10.1007/3-540-33417-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30915-4
Online ISBN: 978-3-540-33417-0
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