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3 results

Distribution in homology classes and discrete fractal dimension
Part of
- Smooth dynamical systems: general theory
- Dynamical systems with hyperbolic behavior
James Everitt, Richard Sharp
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

28 May 2024, pp. 1-8
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In this note, we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.

Pairs of periodic orbits with fixed homology difference
Part of
- Dynamical systems with hyperbolic behavior
- Smooth dynamical systems: general theory
Morten S. Risager, Richard Sharp
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010

Published online by Cambridge University Press:

12 August 2010, pp. 799-808
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We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.

GEOMETRIC ANOSOV FLOWS OF DIMENSION FIVE WITH SMOOTH DISTRIBUTIONS
Yong Fang
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 4 / Issue 3 / July 2005

Published online by Cambridge University Press:

15 April 2005, pp. 333-362

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July 2005
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We classify the five-dimensional $C^\infty$ Anosov flows which have $C^\infty$-Anosov splitting and preserve a smooth pseudo-Riemannian metric. Up to a special time change and finite covers, such a flow is $C^\infty$ flow equivalent either to the suspension of a symplectic hyperbolic automorphism of $\mathbb{T}^{4}$, or to the geodesic flow on a three-dimensional hyperbolic manifold.
AMS 2000 Mathematics subject classification: Primary 34Cxx; 34Dxx; 37-XX

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3 results

Distribution in homology classes and discrete fractal dimension

Pairs of periodic orbits with fixed homology difference

GEOMETRIC ANOSOV FLOWS OF DIMENSION FIVE WITH SMOOTH DISTRIBUTIONS