## 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
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

JMD

We provide sufficient conditions on a positive function so that the associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow. This gives the first such complete classification within the class of Liouville dynamics. This rigidity coexists with a plethora of pathological behaviors.

DCDS-S

We show that given any tiling of Euclidean space, any geometric
pattern of points, we can find a patch of tiles (of arbitrarily
large size) so that copies of this patch appear in the tiling nearly
centered on a scaled and translated version of the pattern. The rather
simple proof uses
Furstenberg's topological multiple recurrence theorem.

DCDS

We consider the dependence on parameters of the solutions of
cohomology equations over Anosov diffeomorphisms. We show that the
solutions depend on parameters as smoothly as the data. As a
consequence we prove optimal regularity results for the solutions of
cohomology
equations taking value in diffeomorphism groups. These results are
motivated by applications to rigidity theory, dynamical systems, and
geometry.

In particular, in the context of diffeomorphism groups we show: Let $f$ be a transitive Anosov diffeomorphism of a compact manifold $M$. Suppose that $\eta \in C$

In particular, in the context of diffeomorphism groups we show: Let $f$ be a transitive Anosov diffeomorphism of a compact manifold $M$. Suppose that $\eta \in C$

^{k+α}$(M,$Diff$^r(N))$ for a compact manifold $N$, $k,r \in \N$, $r \geq 1$, and $0 < \alpha \leq \Lip$. We show that if there exists a $\varphi\in C$^{k+α}$(M,$Diff$^1(N))$ solving$ \varphi_{f(x)} = \eta_x \circ \varphi_x$

then in fact $\varphi \in C$^{k+α}$(M,$Diff$^r(N))$.
The existence of this solutions for some range of regularities is
studied in the literature.

keywords:
Anosov diffeomorphisms
,
Cohomology equations
,
rigidity.
,
diffeomorphism groups
,
Livšic
theory

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]