Additional ressources

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Research additional material:

Maple files for isomonodromic deformations of Painlevé equations (See the article "Hamiltonian representation of isomonodromic deformations of general rational connections on gl_2(C)"). All files (.zip)
- Painlevé 2 case:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
- Painlevé 3 case:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
- Painlevé 4 case:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
- Painlevé 5 case:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
- Painlevé 6 case:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
- Second element of the Painlevé 2 hierarchy:
  1. Computation of the Casimir coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and of the geometric Lax matrices : Maple file, pdf file
  4. Comparing results with theoretical formulas : Maple file, pdf file
  5. Comparing results with H. Chiba Lax pair : Maple file, pdf file
Maple files for isospectral Darboux coordinates in relation with isomonodromic deformations (See the article "Isomonodromic and isospectral deformations of meromorphic connections: the sl2(C) case").
1. Painlevé 2 example:Maple file, pdf file
2. Example of resolution of the differential systems:Maple file, pdf file
Maple files for the article "Explicit Hamiltonian representations of meromorphic connections and duality from different perspectives: a case study"
1. Lax matrices and Hamiltonian systems for the gl_3 case:Maple file, pdf file
2. Lax matrices and Hamiltonian systems for the gl_2 case:Maple file, pdf file
3. Fundamental symplectic two-form for the gl_3 case:Maple file, pdf file
4. Fundamental symplectic two-form for the gl_2 case:Maple file, pdf file
5. JMU differentials and relation with Hamiltonian differentials:Maple file, pdf file
6. Comparing JMU differentials:Maple file, pdf file
7. Spectral duality:Maple file, pdf file
Maple files for isomonodromic deformations of the Painlevé 1 hierarchy (See the article "Hamiltonian representation of isomonodromic deformations of twisted rational connections: The Painlevé 1 hierarchy"). All files (.zip)
- Painlevé 1 case:
  1. Computation of the spectral coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions and decomposition of tangent space : Maple file, pdf file
- Second element of the Painlevé 1 hierarchy:
  1. Computation of the spectral coefficients : Maple file, pdf file
  2. Computation of the Lax matrices in the oper gauge : Maple file, pdf file
  3. Computation of the Hamiltonian evolutions : Maple file, pdf file
  4. Computation of the geometric Lax matrices in symmetric Darboux coordinates : Maple file, pdf file
  5. Computation of the reduced Lax matrices : Maple file, pdf file
- Third element of the Painlevé 1 hierarchy: