摘要
對超大質量雙黑洞星系的動態系統進行研究。此模型是由限制三體問題演變而成，其中星系位能被視為額外加入的能量。在相等質量的雙黑洞條件之下，對不同初始條件的恆星之軌道進行研究。

Abstract
The dynamics of galactic systems with central supermassive binary black holes is studied. The model is a modification from the restricted three body problem, in which a galactic potential is added as an external potential. Considering the case with equal mass binary black holes, the orbits of particles under the galactic potential for different initial conditions are investigated.

Chapter 1 Introduction 1
Chapter 2 The Model 3
Chapter 3 The Equilibrium Points 9
Chapter 4 Simulation Results 12
Section 4.1 Model A: E_0=-H/3,u^2+v^2=H/3 14
Section 4.2 Model B: E_0=-7H/18,u^2+v^2=4H/18 22
Section 4.3 Model C: E_0=-8H/18,u^2+v^2=2H/18 28
Section 4.4 Model D: E_0=-17H/36,u^2+v^2=2H/36 34
Section 4.5 Model E: E_0=-([H])/2,u^2+v^2=H-[H] 40
Chapter 5 The orbit behaviors near the equilibrium points and the black hole 45
Section 5.1 near the equilibrium point L1 45
Section 5.2 near the equilibrium point L2 46
Section 5.3 near the equilibrium point L4 47
Section 5.4 near the equilibrium point JY1 48
Section 5.5 near the black hole of right hand side 49
Chapter 6 Conclusion 51
Section 6.1 Discussion Table 6.1.1. 52
Section 6.2 Summary 54
Bibliography 55
Appendix A: The initial conditions for the case E_0=-H/3 57
Appendix B: The initial conditions for the case E_0=-7H/18 58
Appendix C: The initial conditions for the case E_0=-8H/18 59
Appendix D: The initial conditions for the case E_0=-17H/36 60
Appendix E: The initial conditions for the case E_0=-([H])/2 61
Appendix F: The initial conditions for the initial location at (0,1.07) 62
Appendix G: The program 63
Appendix H: Making gif files by gnuplot 66

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