Related papers: Jean-Christophe Yoccoz and the theory of circle di…

We briefly describe our works in collaboration with Jean-Christophe Yoccoz, a great mathematician and friend, with special emphasis on those related to Homoclinic Bifurcations and Fractal Geometry. We also tell some related personal…

This paper is an introduction to the dynamics of rational fractions over a p-adic field. It follows the lectures that Jean-Christophe Yoccoz gave during the \'Etats de la recherche in May 2006, and develops certain points. Most of the…

We prove two theorems of reduction of cocycles taking values in the group of diffeomorphisms of the circle. They generalise previous results obtained by the author concerning rigidity for smooth actions on the circle of Kazhdan's groups and…

A central problem in the study of critical circle dynamics is understanding the regularity of Yoccoz conjugators - circle homeomorphisms that conjugate critical circle maps with irrational rotation numbers to their corresponding rigid…

This book covers many of the recent results on group actions on the circle, with an emphasis in the differentiable case.

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of…

I review some of the scientific work of George Papadopoulos in the context of the Greek cultural tradition and modern theoretical physics. The main emphasis is on his works on path integrals and their applications. The review is closed by…

We give a survey of Quillen's contributions, apart from the very first joint paper with Loday, to the area of cyclic homology.

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…

These lecture notes contain an exposition of basic ideas of K-theory and cyclic cohomology. I begin with a list of examples of various situations in which the K-functor of Grothendieck appears naturally, including the rudiments of the…

Jean's `Fundamental Theorem of Phyllotaxis' (\emph{Phyllotaxis: a systematic study in Plant Morphogenesis}, CUP 1994) describes the relationship between the count numbers of observed spirals in cylindrical lattices and the horizontal angle…

We describe a geometric theory classified by Connes-Consani's epicylic topos and two related theories respectively classified by the cyclic topos and by the topos $[{\mathbb N}^{\ast}, \mathbf{Set}]$.

A remark about the role of Galois theory in Diophantine geometry as reflected in the work of Serge Lang. An entry in `The mathematical contributions of Serge Lang.'

We will try to give an overview of one of the landmark results of Jorge Lewowicz: his classification of expansive homeomorphisms of surfaces. The goal will be to present the main ideas with the hope of giving evidence of the deep and…

In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.

A survey of Michel Henon contributions to the study of globular cluster systems.

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

This article is an expanded version of some notes for my talk at the ``Ergodic Theory and Dynamical Systems Workshop'' (from March 22 to March 25, 2012) held at the Department of Mathematics of the University of North Carolina at Chapel…

We give a historical perspective on the role of the cyclic category in the development of cyclic theory. This involves a continuous interplay between the extension in characteristic one and in S-algebras, of the traditional development of…