Quadratic volume-preserving maps
نویسندگان
چکیده
منابع مشابه
Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and is also the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with...
متن کاملQuadratic Volume Preserving Maps: an Extension of a Result of Moser
A natural generalization of the Hénon map of the plane is a quadratic diffeomorphism that has a quadratic inverse. We study the case when these maps are volume preserving, which generalizes the the family of symplectic quadratic maps studied by Moser. In this paper we obtain a characterization of tliese maps for dimension four and less. In addition, we use Moser's result to construct a subfamil...
متن کاملQuadratic Volume-preserving Maps: (un)stable Manifolds, Hyperbolic Dynamics, and Vortex-bubble Bifurcations
We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex-bubbl...
متن کاملQuadratic Volume-Preserving Maps: (Un)stable Manifolds, Hyperbolic Dynamics, and Vortex-Bubble Bifurcations
We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex bubbl...
متن کاملHigher Tori in Volume-Preserving Maps
für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 1998
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/11/3/009