Xiaoping Yuan

activity

20062026

most citedA KAM theorem with applications to partial equations of higher dimension

26 citations · 85 across the 32 of their papers we have counts for

collaborators

Showing 2013Show all

6 papers · 1 filter

math.DS2013★ 1 cited

Ergodic properties of invariant measures for systems with average shadowing property

Yiwei Dong, Xueting Tian, Xiaoping Yuan

In this paper, we explore a topological system $f : M \to M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected…

math.SP2013

Absolutely Continuous Spectrum for the Quasi-periodic Schrödinger Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

Avila and Jitomirskaya prove that the quasi-periodic Schrödinger operator $H_{λ v, α, θ}$ has purely absolutely continuous spectrum for $α$ in sub-exponential regime (i.e., $β (α) = 0$ )…

math.SP2013★ 10 cited

Anderson localization for the completely resonant phases

Wencai Liu, Xiaoping Yuan

For the almost Mathieu operator $(H_{λ, α, θ} u) (n) = u (n + 1) + u (n - 1) + λ v (θ + n α) u (n)$ , Avila and Jitomirskaya guess that for every phase $ θ\in \mathscr{R} \triangleq\{θ\in \mathbb{R}\;|…

math.ST2013★ 8 cited

Hölder Continuity of the Spectral Measures for One-Dimensional Schrödinger Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

Avila and Jitomirskaya prove that the spectral measure $μ_{λ v, α, x}^{f}$ of quasi-periodic Schrödinger operator is $1/2$ -Hölder continuous with appropriate initial vector $f$ , if $α$ …

math.SP2013★ 15 cited

Spectral Gaps of Almost Mathieu Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

For almost Mathieu operator $(H_{λ, α, θ} u)_{n} = u_{n + 1} + u_{n - 1} + 2 λ cos 2 π (θ + n α) u_{n}$ , the dry version of Ten Martini problem predicts that the spectrum $Σ_{λ, α}$ of $H_{λ, α, θ}$ has all…

math.SP2013★ 8 cited

Anderson Localization for the Almost Mathieu Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

For the almost Mathieu operator $(H_{λ, α, θ} u)_{n} = u_{n + 1} + u_{n - 1} + 2 λ cos 2 π (θ + n α) u_{n}$ , Avila and Jitomirskaya guess that for a.e. $θ$ , $H_{λ, α, θ}$ satisfies Anderson localization if $…