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Transport problems and disintegration maps

Luca Granieri, Francesco Maddalena (2013)

ESAIM: Control, Optimisation and Calculus of Variations

By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a...

Transversal intersection of separatrices and branching of solutions as obstructions to the existence of an analitic integral in many-dimensional system. I. Basic results: Separatrices of hyperbolic periodic points.

Sergei A. Dovbysh (1999)

Collectanea Mathematica

It is well-known that the existence of transversally intersecting separatrices of hyperbolic periodic solutions leads, in a typical situation, to complicated and irregular dynamics. Therefore, in the case of a two-dimensional mapping or a three-dimensional flow, with this transversality property, there is no non-trivial analytic or meromorphic first integral, i.e., a function constant along each trajectory of the system under consideration. Additional robust conditions are obtained and discussed...

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