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Kähler manifolds with split tangent bundle

Marco Brunella, Jorge Vitório Pereira, Frédéric Touzet (2006)

Bulletin de la Société Mathématique de France

This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.

KAM theory for the hamiltonian derivative wave equation

Massimiliano Berti, Luca Biasco, Michela Procesi (2013)

Annales scientifiques de l'École Normale Supérieure

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.

KAM Tori and Quantum Birkhoff Normal Forms

Georgi Popov (1999/2000)

Séminaire Équations aux dérivées partielles

This talk is concerned with the Kolmogorov-Arnold-Moser (KAM) theorem in Gevrey classes for analytic hamiltonians, the effective stability around the corresponding KAM tori, and the semi-classical asymptotics for Schrödinger operators with exponentially small error terms. Given a real analytic Hamiltonian H close to a completely integrable one and a suitable Cantor set Θ defined by a Diophantine condition, we find a family Λ ω , ω ∈ Θ , of KAM invariant tori of H with frequencies ω ∈ Θ which is Gevrey smooth with...

Kermack-McKendrick epidemic model revisited

Josef Štěpán, Daniel Hlubinka (2007)

Kybernetika

This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale N t that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size N t . Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer...

Kermack-McKendrick epidemics vaccinated

Jakub Staněk (2008)

Kybernetika

This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...

Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow

Luca Marchese (2012)

Bulletin de la Société Mathématique de France

We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.

Kink solutions of the binormal flow

Luis Vega (2003)

Journées équations aux dérivées partielles

I shall present some recent work in collaboration with S. Gutierrez on the characterization of all selfsimilar solutions of the binormal flow : X t = X s × X s s which preserve the length parametrization. Above X ( s , t ) is a curve in ℝ 3 , s ∈ ℝ the arclength parameter, and t denote the temporal variable. This flow appeared for the first time in the work of Da Rios (1906) as a crude approximation to the evolution of a vortex filament under Euler equation, and it is intimately related to the focusing cubic nonlinear Schrödinger...

Kneading sequences for double standard maps

Michael Benedicks, Ana Rodrigues (2009)

Fundamenta Mathematicae

We investigate the symbolic dynamics for the double standard maps of the circle onto itself, given by f a , b ( x ) = 2 x + a + ( b / π ) s i n ( 2 π x ) ( m o d 1 ) , where b = 1 and a is a real parameter, 0 ≤ a < 1.

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