Moser’s Quadratic, Symplectic Map
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
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.
Details
Original language | English |
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Pages (from-to) | 654-664 |
Number of pages | 11 |
Journal | Regular and Chaotic Dynamics |
Volume | 23 |
Issue number | 6 |
Publication status | Published - 12 Dec 2018 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- 34C28, 37C05, 37J40, 70H08, Hénon map, invariant tori, Krein bifurcation, saddle-center bifurcation, symplectic maps