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

• Autorzy: Gianluca Gorni , Gaetano Zampieri
• Języki publikacji: EN

Abstrakty

EN

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 function can be seen as a Lyapunov function for a suitable dynamical system having the lifted paths as trajectories.

Słowa kluczowe

EN

global invertibility; local homeomorphisms; star-shaped sets; line-lifting; Lyapunov functions

Kategorie tematyczne

• 26B10: Implicit function theorems, Jacobians, transformations with several variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 2
• Strony: 171-196

Daty

wydano

1994

otrzymano

1993-05-06

Twórcy

autor

Gianluca Gorni

• Dipartimento di Matematica e Informatica, Università di Udine, via Zanon 6, 33100 Udine, Italy

autor

Gaetano Zampieri

• Dipartimento di Matematica, Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy

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