| Abstract: |
| In this talk we shall discuss the relation between minimality and expansiveness for regular flows. Our main goal is to extend a famous result due Ma\~n\`e which states that if an expansive homeomorphism is minimal, then it must be defined on a zero dimensional space. An attempt of extending this result to flows was made by Keynes and Sears in 1981 with the extra assumption of no spiral points or the flows being Axiom A. Here we will see how remove those extra conditions and obtain a result analogous to Ma\~n\`e`s in full generality. Precisely, we show that a expansive flow is minimal if and only if it is a suspension of a minimal subshift of finite type. We further apply our findings to study the minimal subsets of expansive flows. This is a joint work with Alfonso Artigue. |
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