It's shown that on an n-dimensional LCS Lie group,there exist harmonic sections and left invariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Riemannian metric.M...It's shown that on an n-dimensional LCS Lie group,there exist harmonic sections and left invariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Riemannian metric.Moreover,we determine all the vector fields which are critical points of the energy functional restricted to vector fields of the same length on the n-dimensional pseudo-Riemannian LCS Lie group.展开更多
Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm, and G be a directed system , let T= {T t:t∈G} be asymptotically nonexpansive ty...Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm, and G be a directed system , let T= {T t:t∈G} be asymptotically nonexpansive type mappings on C . We give the weak convergence theorem of {T t:t∈G} in this paper.展开更多
There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = ...There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.展开更多
A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to co...A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to compel the hyperchaotic system to converge into the equilibrium. It is proved theoretically that this control law is feasible and valid by Lyapunov second method. Based on linear feedback synchronization control principle, synchronization control of the novel hyperchaotic system is realized. Numerical simulation shows that this synchronization method is simple and effective. As long as the proper linear feedback control vector is chosen, it is easy to achieve the rapid synchronization between the driving system and response system.展开更多
基金Supported by General Project for the Cultivation of Excellent Young Teachers of Anhui Province(YQYB2024018)。
文摘It's shown that on an n-dimensional LCS Lie group,there exist harmonic sections and left invariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Riemannian metric.Moreover,we determine all the vector fields which are critical points of the energy functional restricted to vector fields of the same length on the n-dimensional pseudo-Riemannian LCS Lie group.
文摘Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm, and G be a directed system , let T= {T t:t∈G} be asymptotically nonexpansive type mappings on C . We give the weak convergence theorem of {T t:t∈G} in this paper.
基金supported by the National Science Center,Poland(Grant No.UMO2014/15/B/ST1/01710)
文摘There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.
文摘A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to compel the hyperchaotic system to converge into the equilibrium. It is proved theoretically that this control law is feasible and valid by Lyapunov second method. Based on linear feedback synchronization control principle, synchronization control of the novel hyperchaotic system is realized. Numerical simulation shows that this synchronization method is simple and effective. As long as the proper linear feedback control vector is chosen, it is easy to achieve the rapid synchronization between the driving system and response system.
