Details

Autor(en) / Beteiligte

• Bernard, Patrick
• Suhr, Stefan

Titel

Lyapounov Functions of Closed Cone Fields: From Conley Theory to Time Functions

Ist Teil von

• Communications in mathematical physics, 2018-04, Vol.359 (2), p.467-498

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We propose a theory “à la Conley” for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of closed (or equivalently semi-continuous) cone fields with singularities. This setting contains (for questions which are parametrization independent such as the existence of Lyapounov functions) the case of continuous vector-fields on manifolds, of differential inclusions, of Lorentzian metrics, and of continuous cone fields. We generalize to this setting the equivalence between stable causality and the existence of temporal functions. We also generalize the equivalence between global hyperbolicity and the existence of a steep temporal function.