Dynamical properties of plane polynomial automorphisms
نویسندگان
چکیده
منابع مشابه
Polynomial composition rigidity and plane polynomial automorphisms
In the first part of this paper, we briefly present a conjecture dealing with polynomial composition and we prove it in some particular cases. In the second and longest part, we prove our main result, which consists of an application of the conjecture to plane polynomial automorphisms. More precisely, we describe the closure of the set of plane polynomial automorphisms having a prescribed multi...
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We obtain normal forms for reversible polynomial automorphisms (i.e., polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized Hénon normal form of Friedland and Milnor, specialized to the case that the map has a polynomial reversor. We show that each such reversor has finite order, and that for nontrivial, real maps, the reversor has order 2 or...
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The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and reversing symmetry groups of a given polynomial automorphism.
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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 Hénon 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 nontrivia...
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Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an involution that is also in the group of polynomial automorphisms. This form is a composition of a sequence of generalized Hénon maps together with two simple involu...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1989
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s014338570000482x