arXiv subjects

Arnaud Girand

Publications and source records attributed to Arnaud Girand.

3 recordsLinked to original sources

arXiv2016

Algebraic isomonodromic deformations of the five punctured sphere arising from quintic plane curves

In this paper, we classify the algebraic isomonodromic deformations that can be obtained through restriction to generic lines of logarithmic flat connections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whose singular locus is a quintic curve. We then explicitly compute the (finite) finite mapping class group orbits of the associated points in the character variety and describe the new algebraic Garnier solutions that can be obtained through this procedure.

math.CV↗

arXiv2016

A new two--parameter family of isomonodromic deformations over the five punctured sphere

The object of this paper is to describe an explicit two--parameter family of logarithmic flat connections over the complex projective plane. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a circle and three tangent lines. By restricting them to generic lines we get an algebraic family of isomonodromic deformations of the five--punctured sphere. This yields new algebraic solutions of a Garnier system. Finally, we use the associated Riccati one--forms to construct an interesting non--generic family of transversally projective Lotka--Volterra foliations.

math.CV↗

arXiv2014

Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution

In this paper, we set up a "dictionary" between discrete Schrödinger operators and the holomorphic dynamics on certain affine cubic surfaces, building on previous work by Cantat, Damanik and Gorodetski. Paragraphs 3.2.2 and 3.2.3 were written by Serge Cantat as an appendix.

math.DS↗