Additional ressources

Administrative material:

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