Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and Podolak’s view of the original theorem. A description of folds in terms of properties of fibers gives new perspective to the usual hypotheses in the subject. The text is intended as a guide, outlining arguments and stating results which will be detailed elsewhere.
Fibers and global geometry of functions / M. Calanchi, C. Tomei, A. Zaccur (PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS). - In: Contributions to nonlinear differential equations and systems : a tribute to Djairo Guedes de Figueiredo on occasion of his 80th Birthday / [a cura di] A.N. Carvalho, B. Ruf, E. Moreira dos Santos, J-P Gossez, S. H.M. Soares, T. Cazenave. - [s.l] : Birkhaeuser, 2015. - ISBN 9783319199016. - pp. 55-75 (( convegno ICMC-Summer Meeting on Differential Equations tenutosi a Sao Carlos nel 2014 [10.1007/978-3-319-19902-3_5].
Fibers and global geometry of functions
M. Calanchi
;
2015
Abstract
Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and Podolak’s view of the original theorem. A description of folds in terms of properties of fibers gives new perspective to the usual hypotheses in the subject. The text is intended as a guide, outlining arguments and stating results which will be detailed elsewhere.File | Dimensione | Formato | |
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