A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorial...A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.展开更多
This paper aims to investigate the retarded Liénard-type equation+f 1(x)+f 2(x)(t-τ)+f 3(x)2+φ(x)+g(x(t-τ))=0,where τ is a nonnegative constant, f 1,f 2,f 3,φ and g are continuous functions on R. Using Liapu...This paper aims to investigate the retarded Liénard-type equation+f 1(x)+f 2(x)(t-τ)+f 3(x)2+φ(x)+g(x(t-τ))=0,where τ is a nonnegative constant, f 1,f 2,f 3,φ and g are continuous functions on R. Using Liapunov functional method, we establish a sufficient condition on the stability and boundedness of the solutions of above equation. This will generalize the main results of reference [2].展开更多
Necessary and sufficient conditions are established for a composition operator C f = fo to be bounded or compact on the Bers-type space Ha and the little Bers-type space Ha The boundedness and compactness of the compo...Necessary and sufficient conditions are established for a composition operator C f = fo to be bounded or compact on the Bers-type space Ha and the little Bers-type space Ha The boundedness and compactness of the composition operator C on A() are characterized, which generalize the case of C on Ha.展开更多
In this paper, we obtain some new necessary and suffcient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.
Let φ be a holomorphic self-map of Bn and ψ∈ H(Bn). A composition type operator is defined by Tψ,φ(f) = ψf o φ for f ∈ H(Bn), which is a generalization of the multiplication operator and the composition operat...Let φ be a holomorphic self-map of Bn and ψ∈ H(Bn). A composition type operator is defined by Tψ,φ(f) = ψf o φ for f ∈ H(Bn), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and suffcient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space Hp(Bn) to μ-Bloch space Bμ(Bn). The conditions are some supremums concerned with ψ, φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.展开更多
This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt...This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).展开更多
The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
This paper is concerned with the boundedness and asymptotic behavior of positive solutions for a generalized difference equation arising from automatic control theory. The main results improve and extend the ones in t...This paper is concerned with the boundedness and asymptotic behavior of positive solutions for a generalized difference equation arising from automatic control theory. The main results improve and extend the ones in the previous works to a large extent. One in particular is that Rouche's theorem is available to prove the convergence of solutions.展开更多
The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in t...The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.展开更多
In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another ...In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.展开更多
令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作...令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作为证明的一个应用,本文也刻m画了算子S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i)的类似性质.展开更多
文摘A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.
文摘This paper aims to investigate the retarded Liénard-type equation+f 1(x)+f 2(x)(t-τ)+f 3(x)2+φ(x)+g(x(t-τ))=0,where τ is a nonnegative constant, f 1,f 2,f 3,φ and g are continuous functions on R. Using Liapunov functional method, we establish a sufficient condition on the stability and boundedness of the solutions of above equation. This will generalize the main results of reference [2].
基金the National Natural Science Foundation of China(19971091)
文摘Necessary and sufficient conditions are established for a composition operator C f = fo to be bounded or compact on the Bers-type space Ha and the little Bers-type space Ha The boundedness and compactness of the composition operator C on A() are characterized, which generalize the case of C on Ha.
基金Supported in part by the National Natural Science Foundation of China(1130140411271359)the Educational Commission of Hubei Province of China(Q20121503)
文摘In this paper, we obtain some new necessary and suffcient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.
基金Supported by NSF of China (10571164)SRFDP of Higher Education (20050358052)
文摘Let φ be a holomorphic self-map of Bn and ψ∈ H(Bn). A composition type operator is defined by Tψ,φ(f) = ψf o φ for f ∈ H(Bn), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and suffcient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space Hp(Bn) to μ-Bloch space Bμ(Bn). The conditions are some supremums concerned with ψ, φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.
基金Supported by the NNSF of China(10771064, 11101139)Supported by the NSF of Zhejiang Province(Y7080197, Y6090036, Y6100219)Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province(T200924)
文摘This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).
基金item： Supported by the National Natural Science Foundation of China（60573040）
文摘The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
基金Supported by the NSF of Universities in Hebei Province(Z2011111)Supported by the Foundation of General Demonstration Course
文摘This paper is concerned with the boundedness and asymptotic behavior of positive solutions for a generalized difference equation arising from automatic control theory. The main results improve and extend the ones in the previous works to a large extent. One in particular is that Rouche's theorem is available to prove the convergence of solutions.
文摘The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.
基金Supported by National Natural Science Foundation of China (No.10971153)
文摘In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.
文摘令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作为证明的一个应用,本文也刻m画了算子S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i)的类似性质.
