1 A problem or scrambled setCHAOTIC behavior is a manifestation of complexity of nonlinear dynamical systems. Since theobjects, methods, aims, or emphases of study are distinct, there are some variant definitionsof ch...1 A problem or scrambled setCHAOTIC behavior is a manifestation of complexity of nonlinear dynamical systems. Since theobjects, methods, aims, or emphases of study are distinct, there are some variant definitionsof chaos given by different authors, or given by the same author in his different works. Thefollowing definition mainly stems from Li and Yorke.展开更多
It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, ...It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.展开更多
In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing propert...In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .展开更多
In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms gi...In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms given are also weakly mixing.展开更多
In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider...In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.展开更多
文摘1 A problem or scrambled setCHAOTIC behavior is a manifestation of complexity of nonlinear dynamical systems. Since theobjects, methods, aims, or emphases of study are distinct, there are some variant definitionsof chaos given by different authors, or given by the same author in his different works. Thefollowing definition mainly stems from Li and Yorke.
文摘It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.
文摘In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .
基金The first author is supported by the Special Foundation of National Prior Basis Research of China(Grant No.G1999075108)the second author is supported by National Natural Science Foundation of China(11171320 and 11431012).
文摘In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms given are also weakly mixing.
基金the Special Foundation of National Prior Basic Researches of China(Grant No.G1999075108)partially supported by the National Natural Science Foundation of China(Grant No.10501042)
文摘In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.
