It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for anal...It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for analytic systems or systems with some degree ofanalytic regularity. In this paper, we disprove the Morse' conjecture for almost every-where analytic C^(∞)-flows on n-dimensional manifolds (n≥2), and prove the validity of theMorse conjecture for analytic flows on T^2.展开更多
This paper introduces generalized ergodicity which contains ergodicity and Lipschitz ergodicity, proves the equivalence relation between generalized ergodicity and chain transitivity and gives its geometrical structure.
文摘It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for analytic systems or systems with some degree ofanalytic regularity. In this paper, we disprove the Morse' conjecture for almost every-where analytic C^(∞)-flows on n-dimensional manifolds (n≥2), and prove the validity of theMorse conjecture for analytic flows on T^2.
基金the National Natural Science Foundation of China (Grant No. 19901034)
文摘This paper introduces generalized ergodicity which contains ergodicity and Lipschitz ergodicity, proves the equivalence relation between generalized ergodicity and chain transitivity and gives its geometrical structure.
