15 citations · 45 across the 17 of their papers we have counts for
19 papers
Multiplicity of topological systems
David Burguet, Ruxi Shi
We define the topological multiplicity of an invertible topological system as the minimal number of real continuous functions such that the functions…
Topological mean dimension of induced systems
David Burguet, Ruxi Shi
For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak- topology has infini…
Maximal measure and entropic continuity of Lyapunov exponents for surface diffeomorphisms with large entropy
David Burguet
We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for surface diffeomorphisms [9]. As a consequence we show that…
SRB measures for C surface diffeomorphisms
David Burguet
A surface diffeomorphism admits a SRB measure if and only if the set \left \{x, \limsup_n \frac{1}{ n} \log \|d_xf^n \|> 0\right\} has positive Lebesgue measure. Moreove…
Zero-dimensional and symbolic extensions of topological flows
David Burguet, Ruxi Shi
A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a…
Mean dimension of continuous cellular automata
David Burguet, Ruxi Shi
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) str…