Journal of the Mathematical Society of Japan

Invariants of two-dimensional projectively Anosov diffeomorphisms and their applications

Masayuki ASAOKA

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Abstract

We define invariants of two dimensional C 2 projectively Anosov diffeomorphisms. The invariants are defined by the topology of the space of circles tangent to an invariant subbundle and are preserved under homotopy of projectively Anosov diffeomorphisms. As an application, we show that the invariant subbundle is not uniquely integrable and two distinct periodic orbits exist if certain invariants do not vanish.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 3 (2007), 603-648.

Dates
First available in Project Euclid: 5 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191591850

Digital Object Identifier
doi:10.2969/jmsj/05930603

Mathematical Reviews number (MathSciNet)
MR2344820

Zentralblatt MATH identifier
1124.37018

Subjects
Primary: 37D30: Partially hyperbolic systems and dominated splittings
Secondary: 37B30: Index theory, Morse-Conley indices 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

Keywords
projectively Anosov systems dominated splittings

Citation

ASAOKA, Masayuki. Invariants of two-dimensional projectively Anosov diffeomorphisms and their applications. J. Math. Soc. Japan 59 (2007), no. 3, 603--648. doi:10.2969/jmsj/05930603. https://projecteuclid.org/euclid.jmsj/1191591850


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References

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