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Sprays and homogeneous connections on 𝐑 × 𝑇𝑀

Alexandr Vondra (1992)

Archivum Mathematicum

The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on R × T M - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.

Structural discontinuities to approximate some optimization problems with a nonmonotone impulsive character

Aldo Bressan, Monica Motta (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In some preceding works we consider a class O P of Boltz optimization problems for Lagrangian mechanical systems, where it is relevant a line l = l γ ( ) , regarded as determined by its (variable) curvature function γ ( ) of domain s 0 , s 1 . Assume that the problem P ~ O P is regular but has an impulsive monotone character in the sense that near each of some points δ 1 to δ ν γ ( ) is monotone and | γ ( ) | is very large. In [10] we propose a procedure belonging to the theory of impulsive controls, in order to simplify P ~ into a structurally...

Structures symplectiques singulières génériques

Spyros N. Pnevmatikos (1984)

Annales de l'institut Fourier

Soit M une variété différentiable de dimension paire munie d’une 2-forme différentielle fermée générique Ω . L’apparition éventuelle d’un lieu de dégénérescence Σ ( Ω ) du rang de Ω est l’obstacle à ce que ( M , Ω ) soit une structure symplectique. Nous étudions les propriétés géométriques de Σ ( Ω ) et nous caractérisons l’algèbre des hamiltoniennes admissibles de ( M , Ω ) i.e. les fonctions différentiables h qui possèdent un champ hamiltonien X h sur M .

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