Journal of the Mathematical Society of Japan

Invariants of two-dimensional projectively Anosov diffeomorphisms and their applications

Masayuki ASAOKA

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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

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

First available in Project Euclid: 5 October 2007

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Zentralblatt MATH identifier

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

projectively Anosov systems dominated splittings


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.

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