Related papers: Dynamics in one complex variable: introductory lec…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…
Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…
In this short note we would like to show how it is possible to use techniques introduced in the theory of local dynamics of holomorphic germs tangent to the identity to study global meromorphic self-maps of the complex projective space. In…
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena,…
We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…
This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time $\tau$. In this work…
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular…
We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it…
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
In the present text we discuss basic aspects of the Seiberg - Witten theory mainly focusing the attantion on some geometrical details which could make the introduction to the subject more illustrative. At the same time we list there natural…