5,193 research outputs found
The resurgent character of the Fatou coordinates of a simple parabolic germ
Given a holomorphic germ at the origin of C with a simple parabolic fixed
point, the local dynamics is classically described by means of pairs of
attracting and repelling Fatou coordinates and the corresponding pairs of horn
maps, of crucial importance for \'Ecalle-Voronin's classification result and
the definition of the parabolic renormalization operator. We revisit \'Ecalle's
approach to the construction of Fatou coordinates, which relies on
Borel-Laplace summation, and give an original and self-contained proof of their
resurgent character.Comment: 7 page
Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow
This paper is a contribution to a program to see symmetry breaking in a
weakly interacting many Boson system on a three dimensional lattice at low
temperature. It provides an overview of our analysis of the "small field"
approximation to the "parabolic flow" which exhibits the formation of a
"Mexican hat" potential well.Comment: 36 page
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