My first collaboration grant project Classifications of Dulac maps and epsilon-neighborhoods,

leader: Maja Resman, co-leader: Pavao Mardesic

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Research topics on the project:

·         geometric description of analytic moduli for Dulac maps and realization

·         resurgent character of the Fatou coordinate of the Dulac map

·         linearization of transseries

 

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ACTIVITIES AND NEWS

Pavao Mardesic, Vesna Zupanovic, Goran Radunovic and Maja Resman at Faculty of Electrical Engineering and Computing during Pavao Mardesic’s visits in November/December 2017

 

 

 

 



  • 22/10/2018-26/10/2018: In the scope of the UKF 'My first collaboration' project 'Classifications of Dulac maps and epsilon-neighborhoods', led by Maja Resman, Faculty of Science, Department of Mathematics, Zagreb, and Pavao Mardešic, Université de Bourgogne, France, Zagreb Dynamical Systems Workshop 2018 was successfully organized at Department of Mathematics of the Faculty of Science from October 22-October 26 2018. The workshop consisted of 13 mini-courses held by prominent foreign experts in various areas of dynamical systems (Abate, Bruin, Crovisier, Gavrilov, Huzak, Mardešic, Novikov, Panazzolo, Rousseau, Teyssier, Yakovenko, Yampolsky, Yomdin) and of 6 research talks of members of our dynamical systems group in Croatia (Dragicevic, Radunovic, Resman, Slijepcevic, Štimac, Županovic). The goals of the workshop were strengthening the area of dynamical systems in Croatia, bringing the area closer to students, exchange of knowledge and new collaborations. The workshop gathered more than 25 participants from Croatia and from abroad. The workshop was opened by the Dean of the Faculty of Science, Professor Aleksandra Cižmešija, the Head of the Department of Mathematics Professor Igor Pažanin and the UKF Program manager Ms Alessia Pozzi. Pavao Mardesic has given a mini-course, and Maja Resman a talk on common research.



    More information about the Workshop, the schedule, as well as some of the presentations from the workshop, can be found at https://web.math.pmf.unizg.hr/Dynsys_workshop_2018/.


  • October 2018
    • P. Mardešic visited Zagreb to work with Maja Resman and Vesna Županovic on submission of the preprint Lengths of epsilon-neighborhoods of Dulac maps and with M. Resman on question of realization of moduli of Dulac maps.

     

     

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    Dissemination activities:

    Talks in seminars/conferences financed by the UKF project:


    07/12/2018: P. Mardesic, La coordonnée de Fatou pour des germes de Dulac (a joint work with J.P. Rolin, M. Resman, V. Zupanovic), Université de Haute-Alsace (Mulhouse), http://www.lmia.uha.fr/LMIA-Universite_de_Haute_Alsace/SeminaireAnalyse (not financed by the project, introductory seminar related to project subject)


    ·         12/04/2018 M. Resman: Classifications of Dulac maps and epsilon-neighborhoods, (seminar talk, joint work with J.P.Rolin, P. Mardesic, V. Zupanovic), Séminaire d’Analyse, Université de Haute Alsace, Mulhouse

    http://www.lmia.uha.fr/LMIA-Universite_de_Haute_Alsace/SeminaireAnalyse.html

     

    ·         10/04/2018 M. Resman: Fatou coordinate for the Dulac germ (seminar talk, joint work with J.P.Rolin, P. Mardesic, V. Zupanovic), Université de Strasbourg IRMA

    http://irma.math.unistra.fr/php/equip_sem.php?equipe=ANA&theme=Analyse&periode=passe

     

    ·         21/06/2018-23/06/2018 M. Resman: The Fatou coordinate of a parabolic Dulac germ (invited conference talk, joint work with J.P.Rolin, P. Mardesic, V. Zupanovic), conference Universality of Resurgence in Quantization Theories, 13 June 2018 - 15 June 2018, Centro di Ricerca Mathematica Ennio de Giorgi, Scuola Normale Superiore, Pisa

    http://www.crm.sns.it/event/433/speakers.html?page=1#title
    https://www.youtube.com/watch?v=W1EfcbAZ4xI&feature=youtu.be

     

    ·         03/09/2018-07/09/2018, M. Resman, Classifications of Dulac maps and epsilon-neighborhoods (joint with Mardesic, Rolin, Zupanovic), Dynamic Days 2018, Loughborough, England,
    http://dynamicsday2018.lboro.ac.uk/MS3.html


    ·         27/08/2018-07/09/2018, P. Mardesic, Can one see a dynamical system by looking at some of its orbits? (joint with Resmam, Rolin, Zupanovic) (not financed by the project), Encuentro de foliaciones y singularidades, Mexico City, Mexico,
    http://www.matem.unam.mx/actividades/otras-actividades/eventos-2018/encuentro-de-foliaciones-y-singularidades/

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    Collaboration stays financed by the project:

    ·         January 2018-June 2018 the project leader stays at University of Burgundy, Dijon, to effectuate the project research with the co-leader Pavao Mardesic and the collaborator Jean-Philippe Rolin (research on geometric description of analytic moduli for Dulac maps and realization question)

     

     

    ·         May 28- June 21 one-month scientific visit of Maja Resman to Ecole Normale Superiore, Pisa (David Sauzin, learning and research on resurgent character of the Fatou coordinate of the Dulac map, conference talk)

     

    ·         May 21-May 28 Universite Paris Diderot (collaboration with Tamara Servi, research on linearization of transseries)

     

    ·         April 09-April 13 Universite de Strasbourg, IRMA (collaboration with Loic Teyssier, research on realization problem for Dulac germs)

     

    ·         December 02-December 18 Universite de Bourgogne, Dijon (collaboration with P. Mardesic, J.P. Rolin, realization problem for the moduli of Dulac maps)

     

     

     

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    Publications (partly) financed by the project:

    ·         preprint Lengths of the epsilon-neighborhoods for Dulac maps submitted to a scientific journal (December 2018)

    Arxiv https://arxiv.org/abs/1606.02581v3

    (partially funded by UKF: the part on reading formal classification of Dulac maps from the initial part of the asymptotic expansion)

     

     

     

    ·         Mardesic, P., Resman, M., Rolin, J.P., Zupanovic, V., The Fatou coordinate for parabolic Dulac germs, Volume 266, Issue 6, 5 March 2019, Pages 3479-3513,
    https://arxiv.org/abs/1710.01268v2
    (important revision in June 2018)

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    Workshop organization (under auspices of UKF, organizers: Maja Resman, Pavao Mardesic)

    Zagreb Dynamical Systems Workshop 2018 (held at Faculty of Science, Department of mathematics, Zagreb, November 22-28 2018).

    January 2018: The lecturers are invited, date fixed and hotel reservations made.

    April 2018: The first announcement is sent by e-mail to many institutions for possibly interested participants.

     

    the web-page of the workshop

     

    the workshop poster