Abstract
We shall consider several aspects related with the global and local behaviour of a 4D symplectic map. In particular, we shall study the Froeschlé map, defined on the 2-annulus (with variables angle-action (x,y)). We shall make different numerical experiments, like: — to represent graphically the rate of escape of the points of the torus “y = 0”, — to compute the intersection between the center-stable (or center-unstable) manifolds of the two EH fixed points and that torus. Different levels of rate are limited by those intersections. 3D invariant manifolds separate different types of behaviour (they are of codimension 1).
-
to represent graphically the rate of escape of the points of the torus “y = 0”,
-
to eompute the intersection between the center-stable (or center-unstable) manifolds of the two EH fixed points and that torus.
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.
References
R. Abraham, J.E. Marsden, T. Ratin. Manifolds, tensor analysis, and applications. Addison-Wesley.
V. Arnold, A. Varchenko, S. Goussein-Zadé. Singularités des applications différentiables (1er parte). Éditions Mir. Moscou
M. Barnsley. Fractals everywhere. Academic Press.
C. Froeschlé. Numerical study of a four-dimensional mapping. Astron. Astrophys. 16, (1972) p. 172.
J. Williamson. On the normal forms of linear canonical transformations in dynamics. Amer. J. Math. 59, pp. 599–617.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Haro, A. (1999). Center and Center-(Un)Stable Manifolds of Elliptic-Hyperbolic Fixed Points of 4D-Symplectic Maps. an Example: the Froeschlé Map. In: Simó, C. (eds) Hamiltonian Systems with Three or More Degrees of Freedom. NATO ASI Series, vol 533. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4673-9_46
Download citation
DOI: https://doi.org/10.1007/978-94-011-4673-9_46
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5968-8
Online ISBN: 978-94-011-4673-9
eBook Packages: Springer Book Archive