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A characterization of isochronous centres in terms of symmetries.

Emilio Freire, Gasull, Armengol, Guillamon, Antoni 2 (2004)

Revista Matemática Iberoamericana

We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity;...

A finite dimensional linear programming approximation of Mather's variational problem

Luca Granieri (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.

A geometric analysis of dynamical systems with singular Lagrangians

Monika Havelková (2011)

Communications in Mathematics

We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.

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