Rescaled entropy of cellular automata

Autor: David Burguet

Publikováno v: Nonlinearity. 34:4897-4922

For a d-dimensional cellular automaton with d $\ge$ 1 we introduce a rescaled entropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent and proves a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::71c246d91ba72a97bd76b7115144526a
https://doi.org/10.1088/1361-6544/abfeab

Uniform Generators, Symbolic Extensions with an Embedding, and Structure of Periodic Orbits

Autor: Tomasz Downarowicz, David Burguet

Publikováno v: Journal of Dynamics and Differential Equations. 31:815-852

For a topological dynamical system $(X, T)$ we define a uniform generator as a finite measurable partition such that the symmetric cylinder sets in the generated process shrink in diameter uniformly to zero. The problem of existence and optimal cardi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bcac314ced1bb290532af302bc17948c
https://doi.org/10.1007/s10884-018-9674-y

Symbolic extensions for 3-dimensional diffeomorphisms

Autor: David Burguet, Gang Liao

We prove that every $\mathcal{C}^{r}$ diffeomorphism with $r>1$ on a three-dimensional manifold admits symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of Downarowicz an

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e9c7be39452e5d0efe9443b536f91ab
https://hal.archives-ouvertes.fr/hal-02346575

Topological and almost Borel Universality for systems with the weak specification property

Autor: David Burguet

Publikováno v: Ergodic Theory and Dynamical Systems
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), In press, ⟨10.1017/etds.2019.7⟩

We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded. This improves, with elementary tools, prev

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4a2649652b216f2669aa24fd1d7795ae
http://arxiv.org/abs/1901.00666

Entropy of Physical Measures for $$C^\infty $$C∞ Dynamical Systems

Autor: David Burguet

Publikováno v: Communications in Mathematical Physics
Communications in Mathematical Physics, Springer Verlag, In press, ⟨10.1007/s00220-019-03516-2⟩

For a $$C^\infty $$ map f on a compact manifold M we prove that for a Lebesgue randomly picked point x there is an empirical measure from x with entropy larger than or equal to the top Lyapunov exponent of $$\Lambda \, df:\Lambda \,TM\circlearrowleft

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3feb4793a8fc259ea9b4114e393be97a
https://hal.archives-ouvertes.fr/hal-02346558