A function associated with spherically convex sets

This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.

Mean Dimension for Non-autonomous Iterated Function Systems

In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension.

Fractional Birkhoffian Dynamics Based on Quasi-fractional Dynamics Models and Its Lie Symmetry

In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.

Mei Symmetry for Constrained Mechanical System on Time Scales

Mei symmetry on time scales is investigated for Lagrangian system,Hamiltonian system,and Birkhoffian system.The main results are divided into three sections.In each section,the definition and the criterion of Mei symmetry are first presented.Then the conserved quantity deduced from Mei symmetry is obtained,and perturbation to Mei symmetry and adiabatic invariant are studied.Finally,an example is given to illustrate the methods and results in each section.The conserve quantity achieved here is a special case of adiabatic invariant.And the results obtained in this paper are more general because of the definition and property of time scale.

时间尺度上Nielsen方程的Mei对称性导致的两类新型守恒量

研究时间尺度上单自由度非迁移完整力学系统Nielsen方程的Mei对称性,及由Mei对称性导致的两类新型Mei守恒量。给出系统的Mei对称性定义和判据方程,得到系统Mei对称性导致的两类新型Mei守恒量的条件和形式,并举例说明结果。

On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations

Assume that f is a transcendental entire function.The ray arg z=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{z_(n)}■J(f)such that lim rn→∞ arg z_(n)=θ.In this paper,we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations F(z)f^(n)(z)+P(z,f)=0,and f^(n)+A(z)P(z,f)=h(z),where P(z,f)is a differential polynomial in f and its derivatives,F(z),A(z)and h(z)are entire functions.We demonstrate the existence of close relationships Petrenko's deviations of the coefficients and the measures of limiting directions of entire solutions of the above two equations.

Topological Pressures on Subsets for Nonautonomous Dynamical Systems

We introduce and study the relation between Pesin-Pitskel topological pressure on an arbitrary subset and measure theoretic pressure of Borel probability measure for nonautonomous dynamical systems,which is an extension of the classical definition of Bowen topological entropy.We show that the Pesin-Pitskel topological pressure can be determined by the local pressures of measures in nonautonomous case and establish a variational principle for Pesin-Pitskel topological pressure on compact subsets in the context of nonautonomous dynamical systems.