Quadratic Volume Preserving Maps

Abstract

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.

Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps)

Cited by in corpus (15)

• Universal Fractional Map and Cascade of Bifurcations Type Attractors
• Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
• Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps
• Resonance Zones and Lobe Volumes for Volume-Preserving Maps
• Accelerator modes and anomalous diffusion in 3D volume-preserving maps
• Homoclinic points of 2-D and 4-D maps via the Parametrization Method
• Nilpotent normal form for divergence-free vector fields and volume-preserving maps
• Visualizing Attractors of the Three-Dimensional Generalized Hénon Map
• Numerical Computation of the Stable and Unstable Manifolds of Invariant Tori
• Anti-Integrability for 3-Dimensional Quadratic Maps
• On interrelations between divergence-free and Hamiltonian dynamics
• Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
• Global Organization of Three-Dimensional, Volume-Preserving Flows: Constraints, Degenerate Points, and Lagrangian Structure
• Stationary Solitons in discrete NLS with non-nearest neighbour interactions
• Topological Dynamics of Volume-Preserving Maps Without an Equatorial Heteroclinic Curve