本論文主要探討二維單參數不可逆動態系統米拉映射驟回排斥子的存在性。我們不難看出米拉映射反可積分極限參數的存在性。根據陳-林-彭結果，可知在反可積分極限附近存在驟回排斥子。本論文以反可積分極限附近為出發點，利用虛擬孤長延拓法與電腦輔助證明，我們可以證明米拉映射在遠離反可積分極限仍存在驟回排斥子。進一步我們由數值結果呈現臨界驟回排斥子的存在性與分歧現象。

In this paper we study the existence of snapback repellers for a 2-dimensional one-parameter noninvertible dynamical system-Mira map. It is not difficult to see the existence of anti-integrable limits. According to the results of Chen-Lin-Peng, they proved the existence of snapback repellers near anti-integrable limits. Employing the pseudo-arclength continuation method and computer-assisted proofs, we prove the existence of snapback repellers on some intervals away from anti-integrable limits. Furthermore, we also show the existence of critical snapback repellers and bifurcation phenomena from our numerical results.

Contents
Abstract(Chinese)i

Abstract(English) ii
Acknowledgements iii

Contents iv

1. Introduction 1

2. Preliminaries 6

2.1 Existence of snapback repellers when parameter values are fixed. ... 9

2.2 Continuation methods and existence of snapback repellers when parameter values are varied. ... 10

3. Study the Existence of Snapback Repellers for Mira map 13

Reference 23

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