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Anosov-Katok Constructions for Quasi-Periodic SL(2,R)Cocycles: 《Peking Mathematical Journal》2024年第1期203-245,共43页Nikolaos Karaliolios Xu Xu Qi Zhou; N.Karaliolios was partially supported by LABEX CEMPI(ANR-11-LABX-0007-01)while a post-doc at Université de Lille;.Q.Zhou was partially supported by National Key R&D Program of China(No.2020YFA0713300);NSFC(Grant No.12071232);The Science Fund for Distinguished Young Scholars of Tianjin(No.19JCJQJC61300);Nankai Zhide Foundation。; We prove that if the frequency of the quasi-periodic SL(2,R)cocycle is Diophantine,then each of the following properties is dense in the subcritical regime:for any 1/2<κ<1,the Lyapunov exponent is exactlyκ-Hölder co...; 关键词：QUASI-PERIODIC Anosov-Katok construction Almost-reducibility

Livšic Theorem for Matrix Cocycles Over An Axiom A Flow: 《Communications in Mathematics and Statistics》2022年第4期681-704,共24页Zeng Lian Jianhua Zhang; partially supported by NNSF of China(11725105,12090012)。; In this paper,we prove a version of Livšic theorem for a class of matrix cocycles over a C^(2)Axiom A flow.As a by-product,an approximative theorem on Lyapunov exponents is also obtained which assets that Lyapunov exp...; 关键词：Matrix cocycles Axiom A flow Lyapunov exponents

Higher Signs for Coxeter Groups: 《Peking Mathematical Journal》2021年第2期285-303,共19页Zhiwei Yun; We define and study cocycles on a Coxeter group in each degree generalizing the sign function.When the Coxeter group is a Weyl group,we explain how the degree three cocycle arises naturally from geometric representati...; 关键词：Coxeter groups COCYCLES Hecke category

Joint Continuity of Lyapunov Exponent for Finitely Smooth Quasi-periodic Schrodinger Cocycles: 《Acta Mathematica Sinica,English Series》2021年第7期1131-1142,共12页Jin Hao LIANG Lin Lin FU; We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schrodinger cocycles with the C^(2)cos-type potentials.In particular,the Lyapunov exponent is log-Holde...; 关键词：Schrodinger cocycle Lyapunov exponent C^(2)cos-type potential

Double Constructions of Frobenius Hom-Algebras and Connes Cocycles: 《Journal of Mathematical Research with Applications》2020年第6期577-595,共19页Shuangjian GUO Lihong DONG; Supported by the National Natural Science Foundation of China(Grant Nos.11761017,11801150);the Science and Technology Foundation of Guizhou Province(Grant No.20201Y005)。; In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the do...; 关键词：Frobenius Hom-algebras Hom-dendriform algebras O-operators antisymmetric infinitesimal Hom-bialgebras Hom-dendriform D-bialgebras

New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies: 《Frontiers of Mathematics in China》2020年第3期467-489,共23页Linlin FU Jiahao XU Fan WU; This work was supported by the National Natural Science Foundation of China(Grant No.11771205).; We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency.We propose a new method to prove that the Lyapunov exponent...; 关键词：Schrodinger cocycle Lyapunov exponent(LE) weak Liouville frequency C2 cos-type potential large deviation theorem(LDT)

Uniform positivity of Lyapunov exponent for a class of smooth Schrodinger cocycles with weak Liouville frequencies被引量：3: 《Frontiers of Mathematics in China》2017年第3期607-639,共33页Jinhao LIANG Po-Jen KUNG; We prove uniform positivity of the Lyapunov exponent for quasiperiodic SchrSdinger cocycles with C2 cos-type potentials, large coupling constants, and fixed weak Liouville frequencies.; 关键词：Lyapunov exponent C2 cos-type potential weak Liouville frequency

On extensions of matrix rings with skew Hochschild 2-cocycles: 《Frontiers of Mathematics in China》2016年第4期869-900,共32页Chan Yong HONG Nam Kyun KIM Tai Keun KWAK Yang LEE; We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we exam...; 关键词：Skew Hochschild extensions matrix rings skew triangular matrix rings （uniquely） clean rings symmetric rings

Structures of Not-finitely Graded Lie Algebras Related to Generalized Heisenberg–Virasoro Algebras被引量：4: 《Acta Mathematica Sinica,English Series》2015年第10期1517-1530,共14页Guang Zhe FAN Chen Hong ZHOU Xiao Qing YUE; Supported by National Natural Science Foundation of China(Grant Nos.11431010,11371278 and 11271284);Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000); In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and th...; 关键词：Not-finitely graded Lie algebras generalized Heisenberg-Virasoro algebras DERIVATIONS AUTOMORPHISMS 2-cocycles

Trivial and Simple Spectrum for SL(d,R) Cocycles with Free Base and Fiber Dynamics: 《Acta Mathematica Sinica,English Series》2015年第7期1113-1122,共10页Mrio BESSA Paulo VARANDAS; Supported by FCT-Fundao para a Ciência e a Tecnologia and CNPq-Brazil(Grant No.PEst-OE/MAT/UI0212/2011); Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（M） is a C^1-Anosov transitive diffeomorphisms and A is an SL（d,R） cocycle dominated with respect to f. We prove that open and densely in ACD...; 关键词：Linear cocycles Lyapunov exponents Anosov diffeomorphisms topological conjugacy maximal entropy measures

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