∞-jets of diffeomorphisms preserving orbits of vector fields

Sergiy Maksymenko

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Controllability on the group of diffeomorphisms

A. A. Agrachev, M. Caponigro (2009)

Annales de l'I.H.P. Analyse non linéaire

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Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.

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Injectivity onto a star-shaped set for local homeomorphisms in n-space

Gianluca Gorni, Gaetano Zampieri (1994)

Annales Polonici Mathematici

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We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary...