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2011-11-06T11:19:36+01:00
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2011-11-06T11:19:36+01:00
2011-11-06T11:19:36+01:00
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Mathematik, Experimentelle Mathematik, Integrable Systeme, Birationale Abbildungen, Diskretisierung
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Bilinear Discretization of Integrable Quadratic Vector Fields: Algebraic Structure and Algebro-Geometric Solutions
Dissertation von Andreas Pfadler
Andreas Pfadler
Dissertation von Andreas Pfadler
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<< /S /GoTo /D (chapter.1) >>
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(Introduction)
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<< /S /GoTo /D (section.1.1) >>
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(Methodological Remarks)
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<< /S /GoTo /D (section.1.2) >>
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13 0 obj
(Outline of the Thesis)
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<< /S /GoTo /D (chapter.2) >>
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(Integrability in the Continuous and Discrete Realm)
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<< /S /GoTo /D (section.2.1) >>
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(Hamiltonian Systems)
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<< /S /GoTo /D (section.2.2) >>
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(Complete Integrability)
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26 0 obj
<< /S /GoTo /D (section.2.3) >>
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29 0 obj
(Integrable Discretizations)
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<< /S /GoTo /D (section.2.4) >>
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33 0 obj
(Detecting and Proving Integrability of Birational Maps)
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34 0 obj
<< /S /GoTo /D (subsection.2.4.1) >>
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37 0 obj
(Algebraic Entropy and Diophantine Integrability)
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<< /S /GoTo /D (subsection.2.4.2) >>
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41 0 obj
(Hirota-Kimura Bases)
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<< /S /GoTo /D (subsection.2.4.3) >>
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(Algorithmic Detection of HK Bases)
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<< /S /GoTo /D (subsection.2.4.4) >>
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(HK Bases and Symbolic Computation)
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<< /S /GoTo /D (subsection.2.4.5) >>
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(Invariant Volume Forms for Integrable Birational Maps)
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<< /S /GoTo /D (subsection.2.4.6) >>
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(Summary)
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<< /S /GoTo /D (chapter.3) >>
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(Elements of the Theory of Elliptic Functions)
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<< /S /GoTo /D (section.3.1) >>
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(Basic Theory)
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<< /S /GoTo /D (section.3.2) >>
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(Relations Between Elliptic Functions And Addition Theorems)
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<< /S /GoTo /D (section.3.3) >>
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(Elliptic Functions, Experimental Mathematics And Discrete Integrability)
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<< /S /GoTo /D (chapter.4) >>
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(The Hirota-Kimura Type Discretizations)
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<< /S /GoTo /D (section.4.1) >>
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(First Integrable Examples)
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<< /S /GoTo /D (subsection.4.1.1) >>
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(Weierstrass Differential Equation)
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<< /S /GoTo /D (subsection.4.1.2) >>
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(Euler Top)
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<< /S /GoTo /D (section.4.2) >>
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(A More Complicated Example: The Zhukovski-Volterra System)
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<< /S /GoTo /D (subsection.4.2.1) >>
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(ZV System with Two Vanishing k's)
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<< /S /GoTo /D (subsection.4.2.2) >>
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(ZV System with One Vanishing k)
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<< /S /GoTo /D (subsection.4.2.3) >>
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(ZV System with All k's Non-Vanishing)
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<< /S /GoTo /D (section.4.3) >>
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(Integrability of the HK type Discretizations)
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<< /S /GoTo /D (chapter.5) >>
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(3D and 4D Volterra Lattices)
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<< /S /GoTo /D (section.5.1) >>
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(Elliptic Solutions of the Infinite Volterra Chain)
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<< /S /GoTo /D (section.5.2) >>
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<< /S /GoTo /D (section.5.3) >>
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(HK type Discretization of VC3)
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<< /S /GoTo /D (section.5.4) >>
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<< /S /GoTo /D (section.5.5) >>
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<< /S /GoTo /D (section.5.6) >>
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(HK type Discretization of VC4)
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<< /S /GoTo /D (section.5.7) >>
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(Solution of the Discrete Equations of Motion)
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<< /S /GoTo /D (chapter.6) >>
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<< /S /GoTo /D (section.6.1) >>
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(Clebsch System)
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<< /S /GoTo /D (subsection.6.1.1) >>
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(First HK Basis)
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<< /S /GoTo /D (subsection.6.1.2) >>
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(Remaining HK Bases)
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(Proof for the Bases 1,2,3)
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<< /S /GoTo /D (section.6.2) >>
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<< /S /GoTo /D (section.6.3) >>
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(Kirchhoff System)
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<< /S /GoTo /D (section.6.4) >>
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<< /S /GoTo /D (chapter.7) >>
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(Conclusion and Future Perspectives)
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<< /S /GoTo /D (appendix.A) >>
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(List of Figures)
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