Héctor E Lomelí and James D Meiss 1998 Nonlinearity 11 557 doi:10.1088/0951-7715/11/3/009
Héctor E Lomelí and James D Meiss
Show affiliationsRecommended 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.
Issue 3 (May 1998)
Received 30 May 1997, in final form 20 January 1998
Héctor E Lomelí and James D Meiss 1998 Nonlinearity 11 557
C Mukku et al 1997 J. Phys. A: Math. Gen. 30 3003
John T Whelan et al 2002 Class. Quantum Grav. 19 1521
J E Nelson 2004 Class. Quantum Grav. 21 S249
R L Rusby and C A Swenson 1980 Metrologia 16 73
Mitio Inokuti and Benjamin Bederson 2006 Phys. Scr. 73 C98
Sandro Wimberger et al 2003 Nonlinearity 16 1381
E G Kalnins 1979 J. Phys. A: Math. Gen. 12 1129
S V Pastukhov 2003 Russ. Math. Surv. 58 187
Dale L Bailey and Antonis Kalemis 2005 Phys. Med. Biol. 50 N55