Invariants of two dimensional projectively Anosov diffeomorphisms. (English) Zbl 1024.37021

Asaoka, Masayuki

Proc. Japan Acad., Ser. A 78, No. 8, 161-165 (2002).

The author defines invariants of two-dimensional projectivity Anosov diffeomorphisms. The author shows that the space of circles tangent to the invariant subbundle has a kind of Morse decomposition. The author proves that the homotopy type of its one point compactification is preserved under any homotopy of projectivity Anosov diffeomorphisms, and presents calculation of the invariants for some examples.

Reviewer: Messoud Efendiev (Berlin)

MSC:

37D20	Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37B30	Index theory for dynamical systems, Morse-Conley indices
37C15	Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37E30	Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces

Keywords:

invariants of homotopy type; Anosov diffeomorphisms; Morse decomposition

References:

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