Abstract
A motion near the separatrix of Hamiltonian systems has fundamental generic features. As was first shown by Poincaré (1892–99) (see also Sect. 7.1.3) any small time-periodic perturbation splits the separatrices corresponding to stable and unstable manifolds which leads to the onset of chaotic motion due to the exponential divergence of orbits with close initial conditions. This phenomenon creates the zone of phase space in the small vicinity of the unperturbed separatrix, so-called a stochastic layer where the motion of system is chaotic (see Sect. 7.1.3).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Abdullaev, S.S. (2006). Mappings Near Separatrix. Theory. 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_5
Download citation
DOI: https://doi.org/10.1007/3-540-33417-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30915-4
Online ISBN: 978-3-540-33417-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)