Affiliation:
1. Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309-0526, USA
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.
Funder
National Science Foundation
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Reference31 articles.
1. A two-dimensional mapping with a strange attractor
2. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences Vol. 42 (Springer-Verlag, New York, 2002).
3. Y. Kuznetsov, Elements of Bifurcation Theory, 3rd ed., Applied Mathematical Sciences Vol. 112 (Springer-Verlag, New York, 2004).
4. THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS
5. Shift automorphisms in the H�non mapping
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