I profited from PRODYN in several ways. First I invited Tyll Krueger and Henk Bruin for visits. The resulting papers from these collaborations are on your web page along with the following preprint:

Also the support of PRODYN allowed me to organize a wonderful ``Workshop on Piecewise Isometries'' whose web page still proudly acknowledges PRODYN's support: http://math.sfsu.edu/goetz/conference/pi/

Here is a list of publications partially sponsored by PRODYN Conferences:

The main stream of research in the interplay between fractal geometry, probability theory and dynamical systems has been devoted for a long time to dynamical systems with invariant hyperbolic probabilities, and has largely ignored those systems with infinite invariant measures or measures describing parabolic or intermittent situations.

During the last years we made progress in
1. Unifying the approach to multifractals and stochastics using Ruelles zeta-function. (kesseb\"ohmer, Denker)
2. Finding new conditions for a function to be aperiodic (no coboundary condition), which does not rely on Leonovs approach. Applications to local limit theorems and the infinite ergodic theory of Fuchsian groups. (Aaronson, Denker, Sarig, Stadlbauer, Zweim\"uller)
3. Thermodynamics in the relative setting given by a factor. (Denker, Gordin, Heinemann, Roy, Schmidt)

The prodyn program was a great opportunity for me as a young researcher. I could attend various meeting organised with the support of this program, where I met the community of searchers working in the area I am interested in. I used the program of short visits in both ditections with Roland Zweimuller (in Erlangen at this time) and Carlangelo Liverani (in Roma) in both directions. I wrote a paper with each of them. Also I appreciated this program as a meeting organiser. The meetings TREC (2000) and L'odyssee Dynamique (2001) got an important amount of money from ESF, and would not have been so intersting without this money.

(in this paper I wrote my thanks to PRODYN for supporting my visit to Dijon in 2000)

Moreover, I would like to mention that I participated in conferences supported by PRODYN (probably): Paris 2001 and Warvick symposia in April and July 2003. My living costs at these conferences and the cost of one trip to Warwick were covered by the organizers. During these two Warwick meetings I worked (with Mariusz Urbanski) on the final version of two papers:

Both papers have been submitted for publication.

Personally, PRODYN allowed me to interact with V. Maume-Deschamps, G.Keller, M.Blank, V.Baladi, M.Bendicks, S.Luzzatto, M.Pollicott with which I have collaborated, and published, or I am collaborating at the moment. In particular, my discussions with M.Pollicott, V.Baldi and M.Bendicks have been instrumental for my work on flows in which exponential decay of correlations is established for all smooth geodesic flows (On Contact Anosov flows, to appear in Annals of Mathematics). More generally, my students and the students of several Italian collegues have greatly benefited from the many activities of PRODYN devoted to the training of young researches. At the european level, I feel that probably the most important achievement of PRODYN is the fact that an entiere new generation of european researched in the field of Dynamical Systems has built professional relations at the european level that, inevitably, will shape their future work in the field. In addition, they have absorbed an image of the field at the european level that has created a common language allowing them to easily communicate across the field subdivisions and the national flavors.

The relevant papers are already on the (new) web page.

The PRODYN grant allowed me to organise a winter school in Switzerland, to participate to several inspiring meetings, in particular in Warwick and Porto (where I could interact both with european and latin american colleagues), and more importantly, to make possible short visits of senior (Benedicks) and younger colleagues (Baillif) with a minimum of hassle. A very important feature of this grant was that the bureaucracy is reduced to a minimum: this is essential to conduct productive research. I must say that I already miss PRODYN, and that I feel very much that the ergodic theoretical community in Europe needs another such grant.

I think it made us aware of the "actors" in the european dynamics scene: there are certainly not more "local nodes" specialising in dynamics, even Orsay, Stockholm and Warwick may lose this title eventually (I hope not). However, there are more and more strong individuals or small clusters scattered all over Europe, and PRODYN allowed them to interact freely and productively.

Papers with PRODYN supported collaborations:

Participation in PRODYN program allowed me to extend of my research to areas connected with smooth ergodic theory (before that I worked only in abstract ergodic theory) and to meet great matematicians. Discussion with them influenced on the progress in my research.

Papers which PRODYN supported (partially):

PRODYN enabled an exchange between Toulouse and Coventry during which the two authors wrote the article.

Due to several mutual short visits in Warwick, Warsaw and Stockholm we have been able to develop a theory of topological Collet-Eckmann maps and a theory of pressure for iteration of rational functions. The following papers resulted:

PRODYN has been instrumental in allowing me to collaborate more closely and more productively with various other researchers in other countries of the program. Important results have been achieved with minimum administrative overhead in the thermodynamical formalism of piecewise expanding maps in higher dimensions.

The following papers are relevant to PRODYN:

I received funding from PRODYN to attend the conference "Dynamical Systems and Ergodic Theory" in Katsiveli (Crimea), 21-30 August 2000.

This conference was of great benefit to my research - in addition to the obvious benefits of attending excellent research talks and minicourses, I was able to advance my collaboration with Andre de Carvalho while there, and also met Nikita Sidorov for the first time, whom I've had many useful conversations with since.

The following papers had some input from discussions taking place during the conference (the first is in the conference proceedings):

PRODYN greatly helped two of my joint research projects by funding a few research visits, in particular for the following paper:

First another reference:

I have benefited from Prodyn in several ways. First by participating to conferences (Warsaw, Cargese) where I had contacts with colleagues and learned new results and techniques. Also a cross visit Geneva/Paris allowed us with J.-P.Eckmann to continue our work on extended systems, developping the theory of extensive quantities like epsilon entropy, topological entropy per unit length, and also the problem of estimating propagation speed of solutions in parabolic systems.

I have benefited a lot from Prodyn and so have many people in France. It was a wonderfull and very successful enterprise and I want to thank and congratulate you personnaly for this success.