On the derivation of a first-order canonical set of hyperbolic Delaunay-type elements.
Luis Floría (1993)
Extracta Mathematicae
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Luis Floría (1993)
Extracta Mathematicae
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Dragović, Vladimir (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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Muslih, S.I. (2002)
Journal of Applied Mathematics
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Ezequiel Maderna (2002)
Bulletin de la Société Mathématique de France
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We show that every global viscosity solution of the Hamilton-Jacobi equation associated with a convex and superlinear Hamiltonian on the cotangent bundle of a closed manifold is necessarily invariant under the identity component of the group of symmetries of the Hamiltonian (we prove that this group is a compact Lie group). In particular, every Lagrangian section invariant under the Hamiltonian flow is also invariant under this group.
Stefano Marmi (1998-1999)
Séminaire Bourbaki
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Diogo A. Gomes, Adam Oberman (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. To do so, we develop a set of explicit estimates for smooth solutions of Hamilton-Jacobi equations, using a combination of methods from viscosity solutions, KAM and Aubry-Mather theories. These estimates are valid in any space dimension, and can be checked numerically to detect gaps between KAM tori and Aubry-Mather sets. We apply these results to detect non-integrable regions in ...
Andrzej J. Maciejewski (2002)
Banach Center Publications
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The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid....
Jean-David Benamou, Philippe Hoch (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
Ignacio Aparicio, Luis Floría (1997)
Extracta Mathematicae
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The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.
Arkadiusz Misztela (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value...
Jean-David Benamou, Philippe Hoch (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We describe both the classical lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
Charles-Michel Marle (2003)
Banach Center Publications
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