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Full-Text Articles in Physical Sciences and Mathematics
Incompressibility And Global Inversion, Eduardo C. Balreira
Incompressibility And Global Inversion, Eduardo C. Balreira
Eduardo Cabral Balreira
Given a local diffeomorphism f : ℝn → ℝn, we consider certain in- compressibility conditions on the parallelepiped D f (x) ([0, 1]n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.
A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, Marius Radulescu, Sorin Radulescu, Eduardo C. Balreira
A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, Marius Radulescu, Sorin Radulescu, Eduardo C. Balreira
Eduardo Cabral Balreira
We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.