[PDF][PDF] Introduction to partially hyperbolic dynamics

S Crovisier, R Potrie - School on Dynamical Systems, ICTP, Trieste, 2015 - Citeseer
These are notes for a minicourse in the School on Dynamical Systems 2015 at ICTP. This
version is quite preliminary, incomplete (mainly in the last sections) and probably contains …

C1 density of stable ergodicity

A Avila, S Crovisier, A Wilkinson - Advances in Mathematics, 2021 - Elsevier
We prove a C 1 version of a conjecture by Pugh and Shub: among partially hyperbolic
volume-preserving C r diffeomorphisms, r> 1, the stably ergodic ones are C 1-dense. To …

Robust criterion for the existence of nonhyperbolic ergodic measures

J Bochi, C Bonatti, LJ Díaz - Communications in Mathematical Physics, 2016 - Springer
We give explicit C 1-open conditions that ensure that a diffeomorphism possesses a
nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the …

What are Lyapunov exponents, and why are they interesting?

A Wilkinson - Bulletin of the American Mathematical Society, 2017 - ams.org
At the 2014 International Congress of Mathematicians in Seoul, South Korea, Franco-
Brazilian mathematician Artur Avila was awarded the Fields Medal for “his profound …

Partially hyperbolic dynamics in dimension three

PD Carrasco, F Rodriguez-Hertz… - Ergodic Theory and …, 2018 - cambridge.org
Partial hyperbolicity appeared in the 1960s as a natural generalization of hyperbolicity. In
the last 20 years, there has been great activity in this area. Here we survey the state of the …

Exponential state estimation, entropy and Lyapunov exponents

C Kawan - Systems & Control Letters, 2018 - Elsevier
In this paper we study the notion of estimation entropy established by Liberzon and Mitra.
This quantity measures the smallest rate of information about the state of a system above …

density of stable ergodicity

A Avila, S Crovisier, A Wilkinson - arXiv preprint arXiv:1709.04983, 2017 - arxiv.org
We prove a $ C^ 1$ version of a conjecture by Pugh and Shub: among partially hyperbolic
volume-preserving $ C^ r $ diffeomorphisms, $ r> 1$, the stably ergodic ones are $ C^ 1 …

A (short) survey on dominated splittings

M Sambarino - Mathematical congress of the Americas, 2016 - books.google.com
In the last two decades, dominated splitting has been playing a central role in the theory of
global dynamics, particularly understanding nonhyperbolic dynamics and extending many …

The entropy of 𝐶¹-diffeomorphisms without a dominated splitting

J Buzzi, S Crovisier, T Fisher - Transactions of the American Mathematical …, 2018 - ams.org
A classical construction due to Newhouse creates horseshoes from hyperbolic periodic
orbits with large period and weak domination through local $ C^ 1$-perturbations. Our main …

Flexibility of Lyapunov exponents

J Bochi, A Katok, FR Hertz - Ergodic Theory and Dynamical Systems, 2022 - cambridge.org
Flexibility of Lyapunov exponents Page 1 Ergod. Th. & Dynam. Sys., (2022), 42, 554–591 ©
The Author(s), 2021. Published by Cambridge University Press. This is an Open Access …