Differential Equations Driven by Moderately Irregular Signals.- The Signature of a Path.- Rough Paths.- Integration Along Rough Paths.- Differential Equations Driven by Rough Paths.

Differential Equations Driven by Rough Paths

Differential geometry on complex and almost complex spaces

This chapter is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a large bibliography.

http://verbit.ru/MATH/Brunella/%5BNessim_Sibony,_Dierk_Schleicher,_Tien-Cuong_Dinh,(BookFi.org).pdf

Holomorphic Dynamical Systems

On the universal covering group of the real symplectic group

https://biblio.ugent.be/publication/4284084/file/4284094.pdf

The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator

Background on Symplectic Spinors.- Symplectic Connections.- Symplectic Spinor Fields.- Symplectic Dirac Operators.- An Associated Second Order Operator.- The Kahler Case.- Fourier Transform for Symplectic Spinors.- Lie Derivative and Quantization.

Introduction to Symplectic Dirac Operators

A Yang–Mills theory in a purely symplectic framework is developed. The corresponding Euler–Lagrange equations are derived and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic connections.

Symplectic Yang–Mills theory, Ricci tensor, and connections

Symplectic Dirac Operators

We give a criterion for the non-degeneracy of the symmetric tensor field on the moduli space of symplectic structures that was introduced in [J. Fricke, L. Habermann, Manuscripta Math. 109 (2002) 405–417] and apply it to nilmanifolds of dimension 6.

On the existence of pseudo-Riemannian metrics on the moduli space of symplectic structures☆

The paper presents an evolutionary game-theoretic approach to open access publishing as an asymmetric game between scientists and publishers. We show how the ordinary differential equations of the model presented can be written as a system of Hamiltonian partial differential equations. The understanding of the setting as a Hamiltonian system implies some properties reflecting the qualitative behavior of the system.

Katharina Habermann

Papers

Introduction to Symplectic Dirac Operators

Symplectic Yang–Mills theory, Ricci tensor, and connections

Symplectic Dirac Operators

On the existence of pseudo-Riemannian metrics on the moduli space of symplectic structures☆

An Evolutionary Game-Theoretic Approach to Open Access