Research

PhD thesis:

Defended: 29/10/2013

Institution: University of Zagreb, Faculty of Science, Department 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 on arXiv, PDF

Research publications:

• Klimes, M., Mardesic, P., Radunovic, G., Resman, M., Analytic invariants of a parabolic diffeomorphism from its orbit , accepted for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2023), arxiv
• Crnkovic, V., Huzak, R., Resman, M., Fractal analysis of hyperbolic saddles with applications , Journal of mathematical analysis and applications, 530 (2024), https://doi.org/10.1016/j.jmaa.2023.127662, arXiv
• Peran, D., Resman, M., Rolin, J.P., Servi, T., Normal forms of hyperbolic logarithmic transseries, Journal of Differential Equations Volume 348 (2023), 154--190, arXiv
• P. Mardešic, G. Radunovic, M. Resman, Fractal zeta functions of orbits of parabolic diffeomorphisms, Analysis and Mathematical Physics, 12, DOI 10.1007/s13324-022-00724-3, pp. 1- 70 (2022); arXiv
• D. Peran, M. Resman, J.P.Rolin, T. Servi, Linearization of complex hyperbolic Dulac germs, Journal of mathematical analysis and applications, 508, pp. 1--27 (2022); arXiv
• Mardesic, P., Resman, M. Realization of analytic moduli for parabolic Dulac germs , Ergodic Theory and Dynamical Systems, First View, pp. 1 - 55 (2021), arXiv
• Mardesic, P., Resman, M. Analytic moduli for parabolic Dulac germs , Russian Math. Surveys (Uspekhi Matematicheskikh nauk), Volume 76 , Number 3 (2021), 389--460 arXiv
• Mardesic, P., Resman, M., Rolin, J.P., Zupanovic, V., Tubular neighborhoods of orbits of Dulac maps , Journal of Dynamics and Differential Equations 1 (2019), 1-49 arXiv
• Mardešić, P., Resman, M., Rolin, J.-P., Županović, V., The Fatou coordinate for parabolic Dulac germs, Journal of Differential Equations 266, 6 (2019), 3479-3513, arXiv
• Mardešić, P., Resman, M., Rolin, J.P., Županovic, V., Normal forms and embeddings for power-log transseries, Advances in Mathematics 303 (2016), 888-953. arXiv
• Resman, M., Epsilon-neighborhoods of orbits of parabolic diffeomorphisms and cohomological equations, Nonlinearity 27 (2014), 3005-3029. arXiv, PDF
• Resman, M., Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms, Discrete and continuous dynamical systems 33 (8) (2013), 3767-3790. arXiv, PDF
• Resman, M., Invariance of the generalized Minkowski content with respect to the ambient space, Chaos, solitons and fractals 57 (2013), 123-128. arXiv, PDF
• Mardešic, P., Resman, M., Zupanovic, V., Multiplicity of fixed points and growth of epsilon-neighborhoods of orbits, Journal of differential equations 253 (8) (2012), 2493-2514. arXiv
• Korkut, L., Resman, M., Oscillations of chirp-like functions, Georgian Mathematical Journal. 19 (4) (2012), 705-720.

Preprints:

• Huzak, R., Mardesic, P., Resman, M., Zupanovic, V., Reading multiplicity in unfoldings from epsilon-neighborhoods of orbits, arXiv, submitted (2023)
• Panazzolo, D., Resman, M., Teyssier, L., Rigidity of saddle loops, submitted (2022), arxiv