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

- 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.

- Peran, D., Resman, M., Rolin, J.P., Servi, T. Normal forms of hyperbolic logarithmic transseries, submitted (2021), arXiv
- D. Peran, M. Resman, J.P.Rolin, T. Servi, Linearization of complex hyperbolic Dulac germs, submitted (2021), arXiv
- P. Mardešic, G. Radunovic, M. Resman, Fractal zeta functions of orbits of parabolic diffeomorphisms, submitted (2020), https://arxiv.org/abs/2010.05955
- Resman, M., Box dimension of a hyperbolic saddle loop and application to cyclicity (2015). arXiv