In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering o...In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.展开更多
For the Hnon map T<sub>a , b</sub>（x, y） = （1- ax<sup>2</sup> + y, bx）, Benedicks and Carleson proved that for （ a, b） near （2, 0） and b 】 0, there exists a set E with positive Lebesgu...For the Hnon map T<sub>a , b</sub>（x, y） = （1- ax<sup>2</sup> + y, bx）, Benedicks and Carleson proved that for （ a, b） near （2, 0） and b 】 0, there exists a set E with positive Lebesgue measure, whose corresponding map T<sub>a,b</sub> possesses a strange attractor. Viana conjectured that if （a, b）∈ E, then the nonwandering set of the map T<sub>a, b</sub>, Ω（Ta, b） = A<sub>a,b</sub> U {q<sub>a, b</sub>},where A（a, b） is the strange attractor, q<sub>a, b</sub> is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E<sub>1</sub> E.展开更多
This paper studies the iteratiolls of holomorphic self-maps which have nonwandering points over general pseudoconvex domains in C2. The authors give especially a Denjoy-Wolff-type theorem on pseudoconvex domains with ...This paper studies the iteratiolls of holomorphic self-maps which have nonwandering points over general pseudoconvex domains in C2. The authors give especially a Denjoy-Wolff-type theorem on pseudoconvex domains with reaLanalytic boundaries, or even more general, on domains of finite type.展开更多
The concept of topological entropy was originally introduced by Adler, Konheim and McAndrew in 1965. Later, Bowen showed a remarkable result, saying that the topological entropy of a self-map of a compact metrizable s...The concept of topological entropy was originally introduced by Adler, Konheim and McAndrew in 1965. Later, Bowen showed a remarkable result, saying that the topological entropy of a self-map of a compact metrizable space equals that of the restrictions of this map on the nonwandering set. One can also find a proof in [3]. All known proofs of this result depend strongly on the metrizability of domains of considered maps. In this note we improve the above Bowen’s result and Show the展开更多
In this note we discuss the Li-Yorke idea on chaos and propose the concept of total chaos. The full proofs of the propositions of this note will appear elsewhere. 1. Since chaos has been discovered, many authors have ...In this note we discuss the Li-Yorke idea on chaos and propose the concept of total chaos. The full proofs of the propositions of this note will appear elsewhere. 1. Since chaos has been discovered, many authors have studied this展开更多
Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) ...Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.展开更多
文摘In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.
文摘For the Hnon map T<sub>a , b</sub>（x, y） = （1- ax<sup>2</sup> + y, bx）, Benedicks and Carleson proved that for （ a, b） near （2, 0） and b 】 0, there exists a set E with positive Lebesgue measure, whose corresponding map T<sub>a,b</sub> possesses a strange attractor. Viana conjectured that if （a, b）∈ E, then the nonwandering set of the map T<sub>a, b</sub>, Ω（Ta, b） = A<sub>a,b</sub> U {q<sub>a, b</sub>},where A（a, b） is the strange attractor, q<sub>a, b</sub> is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E<sub>1</sub> E.
文摘This paper studies the iteratiolls of holomorphic self-maps which have nonwandering points over general pseudoconvex domains in C2. The authors give especially a Denjoy-Wolff-type theorem on pseudoconvex domains with reaLanalytic boundaries, or even more general, on domains of finite type.
基金Project supported by the National Natural Science Foundation of China
文摘The concept of topological entropy was originally introduced by Adler, Konheim and McAndrew in 1965. Later, Bowen showed a remarkable result, saying that the topological entropy of a self-map of a compact metrizable space equals that of the restrictions of this map on the nonwandering set. One can also find a proof in [3]. All known proofs of this result depend strongly on the metrizability of domains of considered maps. In this note we improve the above Bowen’s result and Show the
基金Project supported in part by the Foundation of Advanced Research Centre, Zhongshan University
文摘In this note we discuss the Li-Yorke idea on chaos and propose the concept of total chaos. The full proofs of the propositions of this note will appear elsewhere. 1. Since chaos has been discovered, many authors have studied this
文摘Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.
