Mario Roy
On Gibbs Families for Fibrewise Expansive Systems
Preprint series: Mathematica Gottingensis
MSC:
54H20 Topological dynamics, See also {28Dxx, 34C35, 58Fxx}
28C99 None of the above but in this section
Abstract: We prove that compact fibred systems, whose fibre maps are uniformly open,
expansive and topologically exact, and whose fibres are continuous in the
Hausdorff metric, possess, for every globally continuous, uniformly fibrewise
locally constant potential, a unique Gibbs family of conditional measures on
its fibres. If the system upon observation has only countably many fibres,
then we associate to any continuous potential a Gibbs family, though, this time,
this family may not be unique.
Keywords: Fibred systems, fibrewise expansive, fibrewise expanding, fibrewise Ruelle expanding, Gibbs measures