The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in S (a unital dual R-bimodule) is a 2-cocycle.
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...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（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.展开更多
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...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 exponents of a given ergodic measure can be approximated by those of periodic measures.展开更多
It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic categor...It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus of continuity of the form exp（-l logtlσ） for some 0〈σ〈1.展开更多
Let （X, G（X）, m） be a probability space with a-algebra G（X） and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V...Let （X, G（X）, m） be a probability space with a-algebra G（X） and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m（Zn） 〈 1/n. Let T be an ergodic automorphism of （X, G） preserving m, and A belong to the space of linear measurable symplectic cocycles展开更多
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...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-Holder continuous at each Diophantine frequency.展开更多
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 exp...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 is continuous in energies.In particular,a large deviation theorem is not needed in the proof.展开更多
Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut...Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.展开更多
In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub&g...In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are nonnegative constants, and g(t)∈ C(□;H) is bounded. Motivated by [1] [2], we obtain the existence and stability of synchronizing solution under some convergence condition. By this result, we provide a general approach for guaranteeing the existence and stability of periodic, quasiperiodic or almost periodic solution of the equation.展开更多
This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost per...This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.展开更多
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...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 representation theory.展开更多
The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng...The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.展开更多
In this paper,solutions of the following non-Lipschitz stochastic differential equations driven by G-Brownian motion：Xt=x＋∫^t0b（s,w,Xs）ds＋∫^t0h（s,ω,Xs）ds＋∫^t0σ（s,ω,Xs）dBs are constructed.It is shown th...In this paper,solutions of the following non-Lipschitz stochastic differential equations driven by G-Brownian motion：Xt=x＋∫^t0b（s,w,Xs）ds＋∫^t0h（s,ω,Xs）ds＋∫^t0σ（s,ω,Xs）dBs are constructed.It is shown that they have the cocycle property.Moreover,under some special non-Lipschitz conditions,they are bi-continuous with respect to t,x.展开更多
Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra...Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra will be given. Furthermore, it will be shown that A contains a finite dimensional subbialgebra which is a quasitriangular Hopf algebra if R is a YB-operator.展开更多
Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We gi...Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".展开更多
We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stabl...We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.展开更多
In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C^1 persistently no small angles if and only if f has a dominated splitting of index i o...In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C^1 persistently no small angles if and only if f has a dominated splitting of index i on the C^1 i-preperiodic set P＊^1（f）. To prove this, we mainly use some important conceptions and techniques developed by Christian Bonatti. In the last section, we also give a characterization of the finest dominated splitting for linear cocvcles.展开更多
Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If ...Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. （2） If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤eM if and only if there exists I ≤ R such that N = （0 ：M I）. （3） If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.展开更多
基金the National Natural Science Foundation of China(1 0 0 71 0 4 7)
文摘The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in S (a unital dual R-bimodule) is a 2-cocycle.
基金Supported by FCT-Fundao para a Ciência e a Tecnologia and CNPq-Brazil(Grant No.PEst-OE/MAT/UI0212/2011)
文摘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（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.
基金partially supported by NNSF of China(11725105,12090012)。
文摘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 exponents of a given ergodic measure can be approximated by those of periodic measures.
文摘It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus of continuity of the form exp（-l logtlσ） for some 0〈σ〈1.
文摘Let （X, G（X）, m） be a probability space with a-algebra G（X） and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m（Zn） 〈 1/n. Let T be an ergodic automorphism of （X, G） preserving m, and A belong to the space of linear measurable symplectic cocycles
文摘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-Holder continuous at each Diophantine frequency.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11771205).
文摘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 is continuous in energies.In particular,a large deviation theorem is not needed in the proof.
文摘Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.
文摘In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are nonnegative constants, and g(t)∈ C(□;H) is bounded. Motivated by [1] [2], we obtain the existence and stability of synchronizing solution under some convergence condition. By this result, we provide a general approach for guaranteeing the existence and stability of periodic, quasiperiodic or almost periodic solution of the equation.
基金supported by the State Program of the Republic of Moldova “Multivalued Dynamical Systems, Singular Perturbations, Integral Operators and Non-Associative Algebraic Structures (Grant No. 20.80009.5007.25)”
文摘This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.
文摘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 representation theory.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501552,11871067supported by the National Natural Science Foundation of China under Grant No.11771433the Fund of the Youth Innovation Promotion Association,CAS
文摘The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.
基金supported by the National Natural Science Foundation of China(No.11001051)
文摘In this paper,solutions of the following non-Lipschitz stochastic differential equations driven by G-Brownian motion：Xt=x＋∫^t0b（s,w,Xs）ds＋∫^t0h（s,ω,Xs）ds＋∫^t0σ（s,ω,Xs）dBs are constructed.It is shown that they have the cocycle property.Moreover,under some special non-Lipschitz conditions,they are bi-continuous with respect to t,x.
文摘Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra will be given. Furthermore, it will be shown that A contains a finite dimensional subbialgebra which is a quasitriangular Hopf algebra if R is a YB-operator.
文摘Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".
文摘We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.
文摘In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C^1 persistently no small angles if and only if f has a dominated splitting of index i on the C^1 i-preperiodic set P＊^1（f）. To prove this, we mainly use some important conceptions and techniques developed by Christian Bonatti. In the last section, we also give a characterization of the finest dominated splitting for linear cocvcles.
文摘Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N = （0：M I）. In this paper, we show： （1） If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. （2） If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤eM if and only if there exists I ≤ R such that N = （0 ：M I）. （3） If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.
