Arnd
Bäcker
2018-11
https://link.springer.com/10.1134%2FS1560354718060023
research_article
654-664
Moser’s Quadratic, Symplectic Map
true
articles
2019-04-11T08:22
https://scigraph.springernature.com/explorer/license/
In 1994, Jürgen Moser generalized Hénon’s area-preserving quadratic map to obtain a normal form for the family of four-dimensional, quadratic, symplectic maps. This map has at most four isolated fixed points. We show that the bounded dynamics of Moser’s six parameter family is organized by a codimension-three bifurcation, which we call a quadfurcation, that can create all four fixed points from none. The bounded dynamics is typically associated with Cantor families of invariant tori around fixed points that are doubly elliptic. For Moser’s map there can be two such fixed points: this structure is not what one would expect from dynamics near the cross product of a pair of uncoupled Hénon maps, where there is at most one doubly elliptic point. We visualize the dynamics by escape time plots on 2d planes through the phase space and by 3d slices through the tori.
2018-11-01
en
99a16c1f03186efe21f13b191c8275d3348f215b14d7d355dc87810667429cd2
readcube_id
Pure Mathematics
Department of Applied Mathematics, University of Colorado, 80309 0526, Boulder, CO, USA
University of Colorado Boulder
6
Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062, Dresden, Germany
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187, Dresden, Germany
Max Planck Institute for the Physics of Complex Systems
Meiss
James D.
pub.1110564764
dimensions_id
doi
10.1134/s1560354718060023
1560-3547
1468-4845
Regular and Chaotic Dynamics
Mathematical Sciences
Springer Nature - SN SciGraph project
23