scholarly journals The Teichmüller geodesic flow and the geometry of the Hodge bundle

2011 ◽  
Vol 29 ◽  
pp. 73-95
Author(s):  
Carlos Matheus
Keyword(s):  
Geodesic Flow ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Geodesic Flow

The Teichmuller Geodesic Flow

1986 ◽  
Vol 124 (3) ◽  
pp. 441 ◽  
Author(s):  
William A. Veech
Keyword(s):  
Geodesic Flow ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Geodesic Flow

scholarly journals Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow

2013 ◽  
Vol 120 (1) ◽  
pp. 207-333 ◽  
Author(s):  
Alex Eskin ◽  
Maxim Kontsevich ◽  
Anton Zorich
Keyword(s):  
Lyapunov Exponents ◽  
Geodesic Flow ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Geodesic Flow

scholarly journals Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension

2021 ◽  
Author(s):  
Hamid Al-Saqban ◽  
Paul Apisa ◽  
Alena Erchenko ◽  
Osama Khalil ◽  
Shahriar Mirzadeh ◽  
...  
Keyword(s):  
Hausdorff Dimension ◽  
Geodesic Flow ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Geodesic Flow

scholarly journals A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

2010 ◽  
Vol 31 (4) ◽  
pp. 1043-1071 ◽  
Author(s):  
VÍTOR ARAÚJO ◽  
ALEXANDER I. BUFETOV
Keyword(s):  
Dynamical Systems ◽  
Large Deviations ◽  
Moduli Space ◽  
Geodesic Flow ◽  
Large Deviation ◽  
Suspension Flows ◽  
Abelian Differentials ◽  
Quantitative Recurrence ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Flow

AbstractLarge deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

2011 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Fixed Point ◽  
Symmetric Space ◽  
Heat Kernel ◽  
Geodesic Flow ◽  
Casimir Operator ◽  
Index Theory ◽  
Weighted Sum ◽  
Orbital Integrals ◽  
Hypoelliptic Heat Kernel ◽  
Wave Kernel

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.

scholarly journals The geodesic flow for discrete groups of infinite volume

1986 ◽  
Vol 96 (2) ◽  
pp. 311-311
Author(s):  
Peter J. Nicholls
Keyword(s):  
Geodesic Flow ◽  
Discrete Groups ◽  
Infinite Volume

The algebraic integrability of geodesic flow onSO(4)

1982 ◽  
Vol 67 (2) ◽  
pp. 297-331 ◽  
Author(s):  
M. Adler ◽  
P. van Moerbeke
Keyword(s):  
Geodesic Flow ◽  
Algebraic Integrability
Sign in / Sign up

Export Citation Format

Share Document