Maximal Measure and Entropic Continuity of Lyapunov Exponents for $${\mathcal {C}}^r$$ Surface Diffeomorphisms with Large Entropy

Autor: David Burguet

Publikováno v: Annales Henri Poincaré.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9eb9018e630f1b0a4a72533562cae164
https://doi.org/10.1007/s00023-023-01308-y

Zero-dimensional and symbolic extensions of topological flows

Autor: Ruxi Shi, David Burguet

Publikováno v: Discrete & Continuous Dynamical Systems. 42:1105

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 zero-dimensional flow. Following [Bur19] we deduce that any topologic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23d04c8b471cca3fc564cbb1941b8d5b
https://doi.org/10.3934/dcds.2021148

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