Research

PhD thesis:

 

Defended:  29/10/2013

Institution: University of Zagreb, Faculty of Science, Dept of mathematics

Title: Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits

Supervisors: Pavao Mardesic, IMB, Université de Bourgogne, Dijon, France

                      Vesna Zupanovic, University of Zagreb, Croatia

Full Text, [ArXiv]

 

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Research interests:

  • Complex and real discrete and continuous dynamical systems

  • Fractal analysis of sets in $\mathbb R^n$ (epsilon-neighborhoods of sets, box dimension, Minkowski content)

  • Classifications of germs and of vector fields via fractal analysis of orbits

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Research publications:

                  [arXiv]

             PDF      [ArXiv]

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Preprints:

  • Resman, M., Box dimension of a hyperbolic saddle loop and application to cyclicity (2015), submitted

               [arXiv]         

  • Mardesic, P., Resman, M., Rolin, J.P., Zupanovic, V.: Length of epsilon-neighborhoods of orbits of Dulac maps (preprint, 2016)   [arXiv]

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Seminar talks:

  • Formes normales formelles et plongement dans des flots formels pour des transseries de type puissance-logarithme, Seminaire Géométrie et Systèmes Dynamiques, Institut de Mathématiques, Université de Bourgogne, Dijon, France, February 2016
  • Classifications of germs of diffeomorphisms and fractal properties of their orbits, Dipartimento di Matematica, Università di Pisa, Italy, October 2015
  • є-neighborhoods of orbits and cohomological equations, Seminaire Géométrie et Systèmes Dynamiques, Institut de Mathématiques, Université de Bourgogne, Dijon, France, May 2014
  • є-neighborhoods of orbits and classifications of parabolic diffeomorphisms, Seminaire Equations Differentielles, Institut de Mathématiques de Toulouse, Université de Toulouse, Toulouse, France, June 2013

  • є-neighborhoods of orbits and classifications of parabolic diffeomorphisms, Seminaire Equations Fonctionnelles, IRMA, Université de Strasbourg, Strasbourg, France, May 2013

  • є-neighborhoods of orbits and classifications of parabolic diffeomorphisms,  Séminaire de Géométrie Analytique, IRMAR, Université de Rennes 1, Rennes, Francuska, March 2013

  • є-neighborhoods of orbits and classifications of parabolic diffeomorphisms, Seminaire Géométrie et Systèmes Dynamiques,  Institut de Mathématiques, Université de Bourgogne, Dijon, France, March 2012

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Conference talks:

  • 2016 Summer School on Fractal Geometry and Complex Dimensions, In celebration of the 60th birthday of Michel Lapidus, CalPoly San Luis Obispo, CA, USA, June 21-29 2016, Epsilon-neighborhoods of orbits of some discrete dynamical systems
  • 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17 2016, Normal forms and embeddings for power-log transseries
  • Géométrie Analytique Réelle et Trajectoires de Champs de Vecteurs, CIRM Luminy, 8-12 Juin 2015, Epsilon-neighborhoods of orbits and classifications of parabolic germs (invited talk)
  • Theoretical and computational methods in dynamical systems and fractal geometry, Maribor, Slovenia, April 7-11 2015, Classifications of parabolic germs and epsilon-neighborhoods of orbits (invited talk)
  • Perspectives on Parabolic points in Holomorphic Dynamics, BIRS Workshop, March 29-April 3 2015, Banff, Alberta, Kanada, Classifications of parabolic germs and fractal properties of orbits

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  • European Advanced Studies Conference 2014, Symposium on Differential and Difference Equations 2014, Homburg, Germany, September 05-08 2014, Epsilon -neighborhoods of orbits of parabolic germs and cohomological equations (invited talk)

  • Feuilletages et équations différentielles complexes, CIRM, Marseille, France, October 15-19 2012, Classification of diffeomorphisms and epsilon-neighborhoods of orbits (a poster)

  • 5th Croatian Mathematical Congress, Rijeka, Croatia, June 18-21 2012, Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms

  • First International Meeting PISRS-PISRS Conference 2011-Analysis, Fractal Geometry, Dynamical Systems and Economics, Messina, Italija, November 08-12 2011, Multiplicity of fixed points and growth of epsilon-neighbourhoods of orbits (invited talk)

  • Equadiff Conference 2011, Loughborough, England, August 01-05 2011, Box dimension and cyclicity for planar systems

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For more about our research group, please follow this link:

           Centre for Nonlinear Dynamics (CND), Zagreb