Displaying similar documents to “Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc”

Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.

A. López Almorox, C. Tejero Prieto (2001)

RACSAM

Similarity:

Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Xi Fu, Liulan Li, Xiantao Wang (2012)

Czechoslovak Mathematical Journal

Similarity:

Let G ⊂ 𝐒𝐔 ( 2 , 1 ) be a non-elementary complex hyperbolic Kleinian group. If G preserves a complex line, then G is ℂ -Fuchsian; if G preserves a Lagrangian plane, then G is ℝ -Fuchsian; G is Fuchsian if G is either ℂ -Fuchsian or ℝ -Fuchsian. In this paper, we prove that if the traces of all elements in G are real, then G is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an...

The cubic Szegő equation

Patrick Gérard, Sandrine Grellier (2010)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We consider the following Hamiltonian equation on the L 2 Hardy space on the circle, i ∂ t u = Π ( | u | 2 u ) , where Π is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several...

Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs, Chen Meiri, Peter Sarnak (2014)

Journal of the European Mathematical Society

Similarity:

We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature ( n - 1 , 1 ) is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for n F n - 1 are thin.

Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions

Lorenzo J. Díaz, Katrin Gelfert (2012)

Fundamenta Mathematicae

Similarity:

We study a partially hyperbolic and topologically transitive local diffeomorphism F that is a skew-product over a horseshoe map. This system is derived from a homoclinic class and contains infinitely many hyperbolic periodic points of different indices and hence is not hyperbolic. The associated transitive invariant set Λ possesses a very rich fiber structure, it contains uncountably many trivial and uncountably many non-trivial fibers. Moreover, the spectrum of the central Lyapunov...

On the Picard problem for hyperbolic differential equations in Banach spaces

Antoni Sadowski (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation z x y = f ( x , y , z , z x y ) on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation z x y = f ( x , y , z , z x , z x y ) using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].

Evolution equations with parameter in the hyperbolic case

Jan Bochenek, Teresa Winiarska (1996)

Annales Polonici Mathematici

Similarity:

The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter h ∈ Ω ⊂ ℝ m in the “hyperbolic” case.

Partial hyperbolicity and homoclinic tangencies

Sylvain Crovisier, Martin Sambarino, Dawei Yang (2015)

Journal of the European Mathematical Society

Similarity:

We show that any diffeomorphism of a compact manifold can be C 1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.