Iterative polynomial regularisation of PIV-type: Hamiltonian systems and Newton polygons

2025/10/14 by Marta Dell’Atti, Dell'Atti, Marta, Galina Filipuk +1
Computer Science · Mathematics · #34M55 #Advanced Optimization Algorithms Research #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2510.12378

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We study several polynomial Hamiltonian systems of PIV-type (including the mixed case quasi-PIV), and show that via the iterative process of polynomial regularisation, it is possible to identify the "minimal" Hamiltonian system. The selected Hamiltonian function is associated with the Newton polygon with minimal area and smallest highest total degree.

Citations

• Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence
• Spaces of initial conditions for quartic Hamiltonian systems of Painlevé and quasi-Painlevé type
• Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type
• On an Orbifold Hamiltonian Structure for the First Painleve Equation
• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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