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
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.
