## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

JMD

Given a bi-Lipschitz measure-preserving homeomorphism of a ﬁnite dimensional compact metric measure space, consider the sequence of the
Lipschitz norms of its iterations. We obtain lower bounds on the growth rate of
this sequence assuming that our homeomorphism mixes a Lipschitz function.
In particular, we get a universal lower bound which depends on the dimension of the space but not on the rate of mixing. Furthermore, we get a lower
bound on the growth rate in the case of rapid mixing. The latter turns out to
be sharp: the corresponding example is given by a symbolic dynamical system
associated to the Rudin–Shapiro sequence

DCDS

This paper is a fusion of a survey and a research article. We
focus on certain rigidity phenomena in function spaces associated
to a symplectic manifold. Our starting point is a lower bound
obtained in an earlier paper with Zapolsky for the uniform norm of
the Poisson bracket of a pair of functions in terms of symplectic
quasi-states. After a short review of the theory of symplectic
quasi-states we extend this bound to the case of iterated Poisson
brackets. A new technical ingredient is the use of symplectic
integrators. In addition, we discuss some applications to
symplectic approximation theory and present a number of open
problems.

## Year of publication

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