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