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Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold

Nalini Anantharaman, Stéphane Nonnenmacher (2007)

Annales de l’institut Fourier

We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized....

Hamiltonian Diffeomorphisms and Lagrangian Distributions.

L. Polterovich, M. Bialy (1992)

Geometric and functional analysis

Hamiltonian flows of curves in $G / SO (N)$ and vector soliton equations of mKdV and sine-Gordon type.

Anco, Stephen C. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Hamiltonian loops from the ergodic point of view

Leonid Polterovich (1999)

Journal of the European Mathematical Society

Let $G$ be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $Y$ . A loop $h : S^{1} \to G$ is called strictly ergodic if for some irrational number the associated skew product map $T : S^{1} \times Y \to S^{1} \times Y$ defined by $T (t, y) = (t + α; h (t) y)$ is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group of $G$ can be represented by strictly ergodic loops? We prove existence of contractible strictly ergodic loops for a wide class of symplectic manifolds (for instance for simply connected...

Hamiltonian stability and subanalytic geometry

Laurent Niederman (2006)

Annales de l’institut Fourier

In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function $h$ which is real analytic around a...

Hamiltonian structure and new exact soliton solutions of some Korteweg--de Vries equations.

Gupta, V.G., Sharma, P. (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

Hamiltonian structure of pi hierarchy.

Takasaki, Kanehisa (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Hamiltonian Systems: Generic Properties of Closed Orbits and Local Perturbations.

F. TAKENS (1970)

Mathematische Annalen

Hamiltonian systems, Lagrangian tori and Birkhoffs's theorem.

Misha Bialy, Leonid Polterovich (1992)

Mathematische Annalen

Hamiltonian systems with linear potential and elastic constraints

Maciej Wojtkowski (1998)

Fundamenta Mathematicae

We consider a class of Hamiltonian systems with linear potential, elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.

Hamiltoniens périodiques et images convexes de l'application moment

Thomas Delzant (1988)

Bulletin de la Société Mathématique de France

Hamilton-Jacobi theory and moving frames.

MacArthur, Joshua D., McLenaghan, Raymond G., Smirnov, Roman G. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Hard ball systems are completely hyperbolic.

Simányi, Nándor, Szász, Domokos (1999)

Annals of Mathematics. Second Series

Hard balls gas and Alexandrov spaces of curvature bounded above.

Burago, Dmitri (1998)

Documenta Mathematica

Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps, II

Feliks Przytycki, Mariusz Urbański, Anna Zdunik (1990)

Studia Mathematica

Harmonic properties of the sum-of-digits function for complex bases

Peter J. Grabner, Pierre Liardet (1999)

Acta Arithmetica

Harmonic tori in spheres and complex projective spaces.

F.E. Burstall (1995)

Journal für die reine und angewandte Mathematik

Hartman's theorem for complex flows in the Poincaré domain

John Guckenheimer (1972)

Compositio Mathematica

Harvesting control for a stage-structured predator-prey model with Ivlev's functional response and impulsive stocking on prey.

Liu, Kaiyuan, Chen, Lansun (2007)

Discrete Dynamics in Nature and Society

Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval

Franz Hofbauer (1992)

Studia Mathematica

Let A be a topologically transitive invariant subset of an expanding piecewise monotonic map on [0,1] with the Darboux property. We investigate existence and uniqueness of conformal measures on A and relate Hausdorff and conformal measures on A to each other.

Currently displaying 1 – 20 of 135

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