Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectr...Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.展开更多
In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using...In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A:Math.Theor.,2011,44:505101],the authors obtain that the principal measure of B^n is equal to 1 for each positive integer n.展开更多
文摘Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.
基金supported by YBXSZC20131046the Scientific Research Fund of Sichuan Provincial Education Department under Grant No.14ZB0007
文摘In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A:Math.Theor.,2011,44:505101],the authors obtain that the principal measure of B^n is equal to 1 for each positive integer n.
