Sarkovskii's Theorem And Simple Periodic Orbits

In the first chapter of this thesis some recent works about periodic points of maps on spaces are summarized.In the second chapter of this thesis, we give a new and simple proof of Sarkovskii theorem by combining Sarkovskii theorem with two theorems of simple periodic orbits and one theorem of return orbits organically and simultaneously. In the previous proof of Sarkovskii theorem, authors usually use the method of Markov-Graph. Here, we mainly use " homotopy " method; that is, to analyze the continous movements of some points in the space and the continous movements of corresponding points in the orbits.In addition, we provide a simple proof of the main part of Sarkovskii supplementary theorem, which asserts that F(2n + 3) F(2n + 1) 0 (n G N).