具多重解的自律微分方程鏈回歸集

Abstract

1967年, Strauss和Yorke引介漸進自律微分方程當中的廣義正向極限集。在這篇論文中,我們研究可能不具有惟一解的自律微分方程鏈回歸集。在某些條件底下,我們可以進一步得到鏈回歸集的半不變性。而鏈回歸集和廣義正向極限集之間的關係將會一併探討。

In 1967, Strauss and Yorke introduced the concept of generalized positive limit sets for asymptotic autonomous differential equations. In this thesis, we study chain recurrent sets for autonomous differential equations possibly with multiple solutions. Under certain conditions, we obtain semi-invariance of the chain recurrent set. Relations between chain recurrent sets and generalized positive limit sets are also concerned.