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Sharp phase transitions for the almost Mathieu operator

It is known that the spectral type of the almost Mathieu operator depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency. We study… Expand

A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces

- Jiansheng Geng, J. You
- Mathematics
- 1 March 2006

In this paper, we give a KAM theorem for a class of infinite dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher… Expand

Perturbations of Lower Dimensional Tori for Hamiltonian Systems

- J. You
- Mathematics
- 10 February 1999

Abstract This paper provides a generalized Kolmogorov–Arnold–Moser theorem for lower dimensional tori in Hamiltonian systems, which applies to multiple normal frequency case. The proof is based on… Expand

KAM Tori for 1D Nonlinear Wave Equations¶with Periodic Boundary Conditions

- L. Chierchia, J. You
- Mathematics, Physics
- 20 April 1999

Abstract:In this paper, one-dimensional (1D) nonlinear wave equations
with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an… Expand

Invariant tori and Lagrange stability of pendulum-type equations

- J. You
- Mathematics
- 1 May 1990

Abstract In this paper we prove that the pendulum-type equation x″ + g(t, x) = 0 possesses infinitely many invariant tori whenever g(t, x) has zero mean value on the torus T2, where g(t, x) belongs… Expand

Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems

In this paper, we prove that a quasi-periodic linear differential equation in sl(2,ℝ) with two frequencies (α,1) is almost reducible provided that the coefficients are analytic and close to a… Expand

An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation

- Jiansheng Geng, Xin-dong Xu, J. You
- Mathematics
- 1 April 2011

Abstract We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the two dimensional nonlinear Schrodinger equation i u t − Δ u + | u | 2 u = 0 , t ∈ R , x ∈ T 2… Expand

Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications

In this paper, we prove that any analytic quasi-periodic cocycle close to constant is the Poincaré map of an analytic quasi-periodic linear system close to constant, which bridges both methods and… Expand

KAM tori for higher dimensional beam equations with constant potentials

- Jiansheng Geng, J. You
- Mathematics
- 15 September 2006

In this paper, we consider the higher dimensional nonlinear beam equations with periodic boundary conditions, where the nonlinearity f(u) is a real–analytic function near u = 0 with f(0) = f'(0) = 0… Expand

Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

- Ao Cai, C. Chavaudret, J. You, Qi Zhou
- Mathematics
- 27 June 2017

We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $$C^{k}$$Ck quasi-periodic $$SL(2,{\mathbb {R}})$$SL(2,R) cocycle is 1 / 2-Hölder continuous in the almost reducible… Expand

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