Article
The three-dimensional generalized Hénon map: Bifurcations and attractors Public Deposited
https://scholar.colorado.edu/concern/articles/pc289k83k
- Abstract
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark–Sacker bifurcations, give rise to Arnold tongues in parameter space. Aperiodic attractors include invariant circles and chaotic orbits; these are distinguished by rotation number and Lyapunov exponents. Chaotic orbits include Hénon-like and Lorenz-like attractors, which can arise from period-doubling cascades, and those born from the destruction of invariant circles. The latter lie on paraboloids near the local unstable manifold of a fixed point.
- Creator
- Date Issued
- 2022
- Academic Affiliation
- Journal Title
- Journal Volume
- 32
- Last Modified
- 2024-07-01
- Resource Type
- Rights Statement
- DOI
- ISSN
- 1089-7682
- Language