Reversors and Symmetries for Polynomial Automorphisms of the Plane

Details Reversors and Symmetries for Polynomial Automorphisms of the Plane Reversors and Symmetries for Polynomial Automorphisms of the Plane

2003-04-16

arxiv.org/abs/nlin/0304035v2

Nonlinearity 17: 975-1000 (2004)

Nonlinear Sciences

Chaotic Dynamics

laTeX with 5 figures. Added new sections dealing with symmetries and an extensive discussion of the reversing symmetry groups

Scientific paper

10.1088/0951-7715/17/3/012

We obtain normal forms for symmetric and for reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized \Henon normal form of Friedland and Milnor. We restrict to the case that the symmetries and reversors are also polynomial automorphisms. We show that each such reversor has finite-order, and that for nontrivial, real maps, the reversor has order 2 or 4. The normal forms are shown to be unique up to finitely many choices. We investigate some of the dynamical consequences of reversibility, especially for the case that the reversor is not an involution.

Affiliated with

Also associated with

No associations

Rating

Reversors and Symmetries for Polynomial Automorphisms of the Plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reversors and Symmetries for Polynomial Automorphisms of the Plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reversors and Symmetries for Polynomial Automorphisms of the Plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-608541