This paper provides sufficient conditions for any map $L$, that is strongly piecewise linear relatively to a decomposition of $R^k$ in admissible cones, to be invertible. Namely, via a degree theory argument, we show that when there are at most four convex pieces (or three pieces with at most a non convex one), the map is invertible. Examples show that the result cannot be plainly extended to a greater number of pieces. Our result is obtained by studying the structure of strongly piecewise linear maps. We then extend the results to the $PC^1$ case.

Local inversion of a class of piecewise regular maps / Laura, Poggiolini; Marco, Spadini. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 17(2018), pp. 2207-2224. [10.3934/cpaa.2018105]

Local inversion of a class of piecewise regular maps

Laura Poggiolini;Marco Spadini
2018

Abstract

This paper provides sufficient conditions for any map $L$, that is strongly piecewise linear relatively to a decomposition of $R^k$ in admissible cones, to be invertible. Namely, via a degree theory argument, we show that when there are at most four convex pieces (or three pieces with at most a non convex one), the map is invertible. Examples show that the result cannot be plainly extended to a greater number of pieces. Our result is obtained by studying the structure of strongly piecewise linear maps. We then extend the results to the $PC^1$ case.
17
2207
2224
Laura, Poggiolini; Marco, Spadini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1108631
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