Zobrazeno 1 - 10
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pro vyhledávání: '"Cai, Ao"'
This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb{R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Commun.Math.Phys.1992] and Hou-You [Invent.Math.2012] in respectivel
Externí odkaz:
http://arxiv.org/abs/2403.09132
Autor:
Cai, Ao
This paper serves as an extended road map for our long-term project "Mixed Random-quasiperiodic Cocycles" [arXiv:2201.04745, arXiv:2109.09544, arXiv:2210.16908, 6, 7] with Pedro Duarte and Silvius Klein. Despite exhibiting totally different natures,
Externí odkaz:
http://arxiv.org/abs/2301.06000
This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint H\"older continuity of the maximal Lyapunov exponent as a function of the cocycle and the transition
Externí odkaz:
http://arxiv.org/abs/2212.00174
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a
Externí odkaz:
http://arxiv.org/abs/2210.16908
In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the
Externí odkaz:
http://arxiv.org/abs/2208.06022
We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result is applicable to cocycles corresponding to Schr\"odinger operators wit
Externí odkaz:
http://arxiv.org/abs/2201.04745
We introduce the concept of mixed random-quasiperiodic linear cocycles. We characterize the ergodicity of the base dynamics and establish a large deviations type estimate for certain types of observables. For the fiber dynamics we prove the uniform u
Externí odkaz:
http://arxiv.org/abs/2109.09544
Publikováno v:
In Advances in Mathematics February 2024 438
Autor:
Cai, Ao
We prove that the quasi-periodic Schr\"{o}dinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if the frequency is Diophantine and the potential is sufficiently small in the corresponding $
Externí odkaz:
http://arxiv.org/abs/2103.15525
Autor:
Ren, Zhongyu, Liu, Yining, Cai, Ao, Yu, Yang, Wang, Xiuxiu, Lan, Lan, Guo, Xiaofei, Yan, Hong, Gao, Xinlu, Li, Hanjing, Tian, Yanan, Ji, Haoyu, Chen, Hongyang, Ding, Fengzhi, Ma, Wenya, Wang, Ning, Cai, Benzhi, Yang, Baofeng
Publikováno v:
In European Journal of Pharmacology 15 January 2024 963