Title Page
Contents
ABSTRACT 7
국문초록 8
Chapter 1. Introduction 9
Chapter 2. Preliminaries 12
2.1. Affine and projective varieties 12
2.2. Polynomial maps and the locus of indeterminacy 14
2.3. Dynamical System 18
2.4. Conjugacy of maps and Equivalent Dynamical Systems 19
2.5. Jacobian matrix with its determinant 21
Chapter 3. The critical pods of f 23
Chapter 4. Theoretical observation of the critical pods in dimension 3 29
Chapter 5. Detailed calculation in dimension 3 40
5.1. Case 1. Algebraically stable f. 40
5.1.1. Subcase 1-1. flat f²(L). 44
5.1.2. Subcase 1-2. quadratic f²(L). 45
5.2. Case 2. Algebraic non-stable f 48
5.2.1. Subcase 2-1. a₂,c₃≠0. 49
5.2.2. Subcase 2-2. a₂=0. 51
5.2.3. Subcase 2-3. a₂≠0, c₃=0, a₃=0. 54
5.2.4. Subcase 2-4. a₂≠0, c₃=0, a₃,c₂≠0. 56
Chapter 6. The critical pods in higher dimensions 59
References 67
FIGURE 3.1. Example 4. 25