Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously i...Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.展开更多
We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated co...We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).展开更多
We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously ...We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.展开更多
基金supported by the National Natural Science Foundation of China(10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese ScholarsScientific Research Foundation of Ministry of Human Resources and Social Security for Returned Overseas Chinese Scholars
文摘Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.
文摘We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
基金supported by the Bonn International Graduate School in Mathematics and by the Iniziativa Ticino in Rete.
文摘We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).
文摘We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.
