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Quadratic volume-preserving maps

Héctor E Lomelí and James D Meiss

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Recommended by L P Shil'nikov

We study quadratic, volume-preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Hénon 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.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.10.De Algebraic structures and number theory

MSC

37D45 Strange attractors, chaotic dynamics

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 3 (May 1998)

Received 30 May 1997, in final form 20 January 1998



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