Geodesic
Injectivity onto a star-shaped set for local homeomorphisms in n-space
Annales Polonici Mathematici, Tome 59 (1994) no. 2, pp. 171-196

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap-59-2-171-196
Keywords: global invertibility, local homeomorphisms, star-shaped sets, line-lifting, Lyapunov functions

Gianluca Gorni 1 ; Gaetano Zampieri 1

1 
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Gianluca Gorni; Gaetano Zampieri. Injectivity onto a star-shaped set for local homeomorphisms in n-space. Annales Polonici Mathematici, Tome 59 (1994) no. 2, pp. 171-196. doi: 10.4064/ap-59-2-171-196

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