Journal of the Mathematical Society of Japan

Invariant fiber measures of angular flows and the Ruelle invariant

Takashi INABA and Hiromichi NAKAYAMA

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The Ruelle invariants for non-singular flows of a 3-dimensional manifold and diffeomorphisms of the disc are described by invariant fiber measures, which are families of probability measures on the fibers of the projectivized bundle invariant under the holonomies among almost all fibers. The dynamical properties of invariant fiber measures are also given, which show the benefit of this description.

Article information

J. Math. Soc. Japan, Volume 56, Number 1 (2004), 17-29.

First available in Project Euclid: 3 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37C40: Smooth ergodic theory, invariant measures [See also 37Dxx]
Secondary: 37E45: Rotation numbers and vectors 37B20: Notions of recurrence 37C10: Vector fields, flows, ordinary differential equations

Ruelle invariant angular flow invariant fiber measure


INABA, Takashi; NAKAYAMA, Hiromichi. Invariant fiber measures of angular flows and the Ruelle invariant. J. Math. Soc. Japan 56 (2004), no. 1, 17--29. doi:10.2969/jmsj/1191418693.

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