關於Henon映射混沌區域的估計量

Abstract

我們研究二次微分同胚 的總體行為。在固定b之後，我們可以把Henon映射轉化成差分方程式 ，此時 為參數。當 ，差分方程式 可以簡化成雙符號的全轉移，我們研究從這種狀態延續的軌跡。首先，我們證明 是混沌的並且在微小的擾動之後，此系統仍會滿足混沌的充分條件，亦即當 足夠靠近 ， 會是混沌。在這篇論文中，我們估計 使得 為混沌，並由此去得到Henon映射的混沌區域。

We investigate the global behavior of the quadratic diffeomorphism of the plane given by . If we fix b, the Henon map can be considered as , a difference equation, where α is the parameter. For α =0, the difference equation, , reduces to the full shift on two symbols, and we study orbits that continues from these states. We first show that the system H0 is chaotic and under a small perturbation, the system satisfies the sufficient condition of chaos, that is for α close enough to zero, Hα display chaotic dynamics. In this paper, we estimate for which α, Hα display chaotic to get the chaotic region for the Henon map.