## Journal of the Mathematical Society of Japan

### Invariants of two-dimensional projectively Anosov diffeomorphisms and their applications

Masayuki ASAOKA

#### 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

https://projecteuclid.org/euclid.jmsj/1191591850

Digital Object Identifier
doi:10.2969/jmsj/05930603

Mathematical Reviews number (MathSciNet)
MR2344820

Zentralblatt MATH identifier
1124.37018

#### 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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