Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 359, Issue 2, Pages 467-498Publisher
SPRINGER
DOI: 10.1007/s00220-018-3127-7
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Funding
- European Research Council under the European Union's Seventh Framework Programme/ERC [307062]
- DFG [SFB/TRR 191]
- European Research Council (ERC) [307062] Funding Source: European Research Council (ERC)
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We propose a theory A 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.
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