## 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

DCDS

In this note, it is shown that some Hamiltonian partial
differential equations such as semi-linear Schrödinger
equations, semi-linear wave equations and semi-linear beam
equations are partially integrable, i.e., they possess integrable
invariant manifolds foliated by invariant tori which carry
periodic or quasi-periodic solutions. The linear stability of the
obtained invariant manifolds is also concluded. The proofs are
based on a special invariant property of the considered equations
and a symplectic change of variables first observed in [26].

DCDS

In this paper, we consider the analytic reducibility problem of an
analytic $d-$dimensional quasi-periodic cocycle $(\alpha,\ A)$ on
$U(n)$ where $ \alpha$ is a Diophantine vector. We prove that, if
the cocycle is conjugated to a constant cocycle $(\alpha,\ C)$ by a
measurable conjugacy $(0,\ B)$, then for almost all $C$ it is
analytically conjugated to $(\alpha,\ C)$ provided that $A$ is
sufficiently close to some constant. Moreover $B$ is actually
analytic if it is continuous.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]