Geodesic
Injectivity onto a star-shaped set for local homeomorphisms in n-space
Annales Polonici Mathematici, Tome 59 (1994) no. 2, pp. 171-196
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_ap_59_2_171_196,
     author = {Gianluca Gorni and Gaetano Zampieri},
     title = {Injectivity onto a star-shaped set for local homeomorphisms in n-space},
     journal = {Annales Polonici Mathematici},
     pages = {171--196},
     year = {1994},
     volume = {59},
     number = {2},
     doi = {10.4064/ap-59-2-171-196},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-59-2-171-196/}
}
TY  - JOUR
AU  - Gianluca Gorni
AU  - Gaetano Zampieri
TI  - Injectivity onto a star-shaped set for local homeomorphisms in n-space
JO  - Annales Polonici Mathematici
PY  - 1994
SP  - 171
EP  - 196
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-59-2-171-196/
DO  - 10.4064/ap-59-2-171-196
LA  - en
ID  - 10_4064_ap_59_2_171_196
ER  - 
%0 Journal Article
%A Gianluca Gorni
%A Gaetano Zampieri
%T Injectivity onto a star-shaped set for local homeomorphisms in n-space
%J Annales Polonici Mathematici
%D 1994
%P 171-196
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-59-2-171-196/
%R 10.4064/ap-59-2-171-196
%G en
%F 10_4064_ap_59_2_171_196
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

Cité par Sources :