Expensive topological $\mathbb{R}$-flows were introduced by Bowen and
Walters in 1972. They proved that such a flow admits an extension by a
suspension flow over a subshift, known in this context as a symbolic
flow, and asked if the extension may be made entropy preserving. In
2019 Burguet solved the problem under smoothness conditions. We solve
the problem in general and show the stronger statement that any
expansive topological flow admits a strongly isomorphic symbolic
extension. Here strongly isomorphic means that up to removing a
dynamically negligible set the extension is simultaneously injective
for all flow invariant measures.

Joint work with Ruxi Shi.

Meeting ID: 852 4277 3200
Passcode: 103121