Journal of the Mathematical Society of Japan

Invariant fiber measures of angular flows and the Ruelle invariant

Takashi INABA and Hiromichi NAKAYAMA

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418693

Digital Object Identifier
doi:10.2969/jmsj/1191418693

Mathematical Reviews number (MathSciNet)
MR2023451

Zentralblatt MATH identifier
1049.37015

Subjects
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

Keywords
Ruelle invariant angular flow invariant fiber measure

Citation

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. https://projecteuclid.org/euclid.jmsj/1191418693


Export citation