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We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form $H = 1 / 2 \sum_{i = 1}^{n} p ²_{i} + V (q)$ , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form $V = V_{k} + V_{K}$ , where $V_{k}$ and $V_{K}$ are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable...

Periodic solutions for a class of autonomous hamiltonian systems

H. Beirão da Veiga (1990)

Rendiconti del Seminario Matematico della Università di Padova

Periodic solutions for second order Hamiltonian systems

Qiongfen Zhang, X. H. Tang (2012)

Applications of Mathematics

By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.

Periodic solutions for second-order Hamiltonian systems with a p -Laplacian

Xianhua Tang, Xingyong Zhang (2010)

Annales UMCS, Mathematica

In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.

The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

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On the problem of stability for near to integrable Hamiltonian systems.

On the question of stability in a Hamiltonian system

On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space.

Orbites périodiques de systèmes conservatifs

Orbites périodiques des systèmes hamiltoniens autonomes

Orbites périodiques d'un système hamiltonien du voisinage d'un point d'équilibre

Oscillations de systèmes hamiltoniens non linéaires. III

Oscillations forcées de systèmes hamiltoniens non linéaires

Overview of the differential Galois integrability conditions for non-homogeneous potentials

Periodic solutions for a class of autonomous hamiltonian systems

Periodic solutions for second order Hamiltonian systems

Periodic solutions for second-order Hamiltonian systems with a p -Laplacian

Periodic solutions of a non coercive Hamiltonian system.

Periodic Solutions of Asymptotically Linear Hamiltonian Systems.

Periodic solutions of some problems of 3-body type

Perturbation of Hamiltonian Systems with Keplerian Potentials.

Perturbations of Systems Describing the Motion of a Particle in Central Fields

Problème diophantien des moments et modèle d'Ising

Problème diophantien des moments et modèle d'Ising

Quadratic Integrals of Linear Hamiltonian Systems.

Currently displaying 81 – 100 of 141