摘要
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.
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<sup>∞</sup>-flows on n-dimensional manifolds （n≥2）, and prove the validity of theMorse conjecture for analytic flows on T<sup>2</sup>.
