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We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.

Affine Parts of Abelian Surfaces as Complete Intersections of Four Quadrics.

W. Barth (1987)

Mathematische Annalen

Algèbres différentielles en théorie des champs

Raymond Stora (1987)

Annales de l'institut Fourier

Les algèbres différentielles sont apparues comme des outils commodes ou même inévitables pour exprimer les symétries continues, exactes ou brisées, suivant la situation physique envisagée, dans le cadre de l’algorithme de Feynman de la théorie quantique des champs perturbative. Les algèbres de courants, les théories de Yang-Mills, la première quantification de la corde, sont proposées comme exemples classiques.

Almost Kenmotsu $f$ -manifolds.

Falcitelli, Maria, Pastore, Anna Maria (2007)

Balkan Journal of Geometry and its Applications (BJGA)

An integrable flow on a family of Hilbert Grassmannians.

Gomez, Rodrigo P. (1996)

The New York Journal of Mathematics [electronic only]

Axial Isometries of Manifolds of Non-Positive Curvature.

Werner Ballmann (1982)

Mathematische Annalen

Billards en polygones et groupes fuchsiens

Eugène Gutkin (1995/1996)

Séminaire de théorie spectrale et géométrie

Bound states in completely integrable systems with two types of particles

M. A. Olshanetsky, V.-B. K. Rogov (1978)

Annales de l'I.H.P. Physique théorique

Brownian motion on a surface of negative curvature

Wilfrid S. Kendall (1984)

Séminaire de probabilités de Strasbourg

Canonical forms for $𝒮_{n - 3}$ -structures in pseudo-riemannian manifolds

Sergio Benenti, Mauro Francaviglia (1979)

Annales de l'I.H.P. Physique théorique

Closed geodesics, periods and arithmetic of modular forms.

Svetlana Katok (1985)

Inventiones mathematicae

Cohomologie bornée des surfaces et courants géodésiques

Jean-Claude Picaud (1997)

Bulletin de la Société Mathématique de France

Collective geodesic flows

Léo T. Butler, Gabriel P. Paternain (2003)

Annales de l’institut Fourier

We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.

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