Pristupačnost
- Bibliography (CROSBI)
- List of select publications
- Teaching
- Research areas
- Personal data
- List of select projects
Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations
MERIA scenario: ellipse and application in astronomy
Oscillatory Integrals and Fractal Dimension
Fractal analysis of planar nilpotent singularities and numerical applications
Group Delay of Fractional n+α-Order Bessel Filters
Mathematical-physical journal, yesterday, today, tomorrow
Mathematical modeling with linear function: multivitamin, taxi and velocity
The Fatou coordinate for parabolic Dulac germs
Formal classification of parabolic Dulac maps
Classifications of Dulac germs
Tubular neighborhoods of orbits of power- logarithmic germs
Classifications of Dulac maps and epsilon-neighborhoods
Classifications of Dulac germs
Introduction to fractal analysis of orbits of dynamical systems
The Fatou coordinate of a parabolic Dulac germ
Fractal properties of a class of polynomial planar systems having degenerate foci
Epsilon-NEIGHBORHOODS OF ORBITS OF DYNAMICAL SYSTEMS
Normal forms and embeddings for power-log transseries
Normal forms and embeddings for power-log transseries
Epsilon-neighborhoods of orbits of some discrete dynamical systems
Fractal Geometry of Oscillatory Integrals and Singularities of Differentiable Maps
Computer supported applied mathematics
Wavy spirals and their fractal connection with chirps
Fractal properties of Bessel functions
Fractal Properties of Oscillatory Integrals and Singularities of Differentiable Maps
Mathematics 2
Geometrical properties of systems with spiral trajectories in R^3
Characteristic box dimension of Poincare map of nilpotent focus
Fractal analysis of bifurcations of dynamical systems
Oscillatory Integrals and Fractal Dimension
Formal normal forms and formal embeddings into flows for power-log transseries
Particle’s Trajectory – Implementation in Maritime Traffic
Characteristic box dimension of unit-time map near nilpotent singularity of planar vector field and applications
Stability of BAM neural network
Fractal dimensions of oscillatory integrals
Fractal Analysis of unit-time map and cyclicity of nilpotent singularities of planar vector fields
Mathematics 1
Project RADDAR
Fractal analysis of unit time map and cyclicity of nilpotent singularities of planar vector field
Multiplicity of fixed points and growth of epsilon- neighborhoods of orbits
Phase dimension of oscillatory solutions of a class of ordinary differential equations with applications
Fractal properties of generalized Bessel functions
Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits
The particle’s trajectory - Implementation
Mathematics for curious RADDAR
Fractal properties of oscillatory solutions of a class of ordinary differential equations
Oscillatority of Fresnel integrals and chirp-like functions
Multiplicity of fixed points and growth of ε-neighborhoods of orbits
Fractal analysis of Hopf bifurcation at infinity
Multiplicity of fixed points and growth of varepsilon-neighbourhoods of orbits
Mathematical and Computer Modelling of Lotka- Volterra Systems
Fractal properties of Bessel equation
Multiplicity of Fixed Points and Growth of r- Neighborhoods of Orbits
Fractal analysis of bifurcations of discrete dynamical systems and applications to continuous systems
Fractal properties of solutions of differential equations
Analysis of bifurcations of a class of neural networks
Connection between box dimension and cyclicity for planar systems
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schroedinger Cauchy problems
Lorenz attractor
Box dimension and Minkowski content of the clothoid
Celebrating 90th anniversary of the Department of Applied Mathematics of FER in Zagreb
Oscillatory and phase dimensions of solutions of some second-order differential equations
Mathematical pendulum
Differential equations and stability theory
Poincare map in fractal analysis of spiral trajectories of planar vector fields
The existence of positive solutions of polyharmonic equations with strong dependence on the gradient
Generalized Fresnel integrals and fractal properties of related spirals
Positive solutions of polyharmonic equations with strong dependence on the gradient
Positive solutions of polyharmonic equations with strong dependence on the gradient
Box dimension of spiral trajectories of some vector fields in R^3
Recent results on fractal analysis of trajectories of some dynamical systems
Multiple integrals
Box dimension of trajectories of some discrete dynamical systems
Fractal analysis of spiral trajectories of some vector fields in ${; ; ; \mathbb R}; ; ; ^3$
Fractal analysis of dynamical systems
Fractal dimensions in dynamics
Fractal analysis of spiral trajectories of some planar vector fields
Fractal analysis of spiral trajectories of some planar vector fields
Box dimensions and Minkowski contents of spiral trajectories
Some metric-singular properties of the graph of solutions of the one-dimensional p-Laplacian
The dynamics of some cubic vector fields with a center
Topological Equivalence of Planar Vector Fields and Their Generalised Principal Part
The principal part of planar vector fields
Generalised principal part of some planar vector fields
- P. Mardešić, M. Resman, J.-P. Rolin, V. Županović, The Fatou coordinate for parabolic Dulac germs, Journal of Differential Equations, 266, Issue 6, 5 March (2019), Pages 3479-3513 Q1 5%, 17/310 Math.
- P. Mardešić, M. Resman, J.-P. Rolin, V. Županović, Normal forms and embeddings for power-log transseries, Advances in mathematics. 303 (2016), 888-953, Q1 10%, 33/310 Math.
- L. Korkut, D. Vlah, V. Županović, Fractal properties of Bessel functions. Appl. Math. Comput. 283 (2016), 55–69 Q1 8%, 21/252 Math. Appl.
- P. Mardešić, M. Resman, V. Županović, Multiplicity of fixed points and growth of ε-neighbor. of orbits, Journal of Differential Equations 253, 8 (2012), 2493–2514 Q1 5%, 17/310 Math
- L. Korkut, D. Vlah, D. Žubrinić, V. Županović, Generalized Fresnel integrals and fractal properties of related spirals, Appl. Math. Comput. 206 (2008) Q1 8%, 21/252 Math. Appl.
- D. Žubrinić, V. Županović, Poincaré map in fractal analysis of spiral trajectories of planar vector fields. Bull of the Belgian Mathematical Society - Simon Stevin. 15, dedicated to Freddy Dumortier 60th birthday (2008), 5; 947-960,
- V. Županović, D. Žubrinić, Fractal dimensions in dynamics, in Encyclopedia of Mathematical Physics, Jean-Pierre Françoise, Greg Naber, Sheung Tsun Tsou (editors), Elsevier Oxford (2006) Vol. 2, 394-402 (Invited paper)
- V. Županović, Topological Equivalence of Planar Vector Fields and Their Generalised Principal Part, Journal of Differential Equations 167, (2000), 1-15 Q1 5%, 17/310 Math.
Teaching
University undergraduate
- Dynamical Systems, Mathematical Aspect of Stability and Control (Lecturer in charge, Lecturer in charge)
- Dynamical Systems, Mathematical Aspect of Stability and Control (Lecturer in charge)
- Mathematical Analysis 3 (Lecturer in charge)
- Mathematical Analysis 3 (Lecturer in charge)
- BSc Thesis (Lecturers)
- BSc Thesis (Lecturers)
- Project (Lecturers)
- Project C (Lecturers)
- Software Design Project (Lecturers)
- Software Design Project (Lecturers)
University graduate
- Differential Equations in Biology and Medicine (Lecturer in charge)
- Graduation Thesis (Lecturers)
- Project (Lecturers)
- Project (Lecturers)
- Seminar (Lecturers)
Postgraduate doctoral study programme
- Differential Equations and Dynamical Systems (Lecturer in charge)
- Mathematical Methods in Control Theory (Lecturer in charge)
- Research seminar in control engineering and automation 1 (Lecturer in charge)
- Research seminar in control engineering and automation 2 (Lecturer in charge)
- Research seminar in control engineering and automation 3 (Lecturer in charge)
- Research seminar in control engineering and automation 4 (Lecturer in charge)
- Research seminar in control engineering and automation 5 (Lecturer in charge)
- Research seminar in control engineering and automation 6 (Lecturer in charge)
Competences
-
Mathematics
Nonlinear equations Bifurcation Fractals Limit-cycles Nonlinear dynamical systems Spirals -
Mathematics
Nonlinear equations Bifurcation Fractals Limit-cycles Nonlinear dynamical systems Spirals
Personal data
List of select projects
1. Classification of fixed points and singularities by e-neighborhoods of orbits and curves
2015– 2016, bilateral Croatian-French Cogito Hubert Curien project, Leader Vesna Županović, French leader Pavao Mardešić
2. Fractal analysis of Poincaré map near polycycle
2011– -2012, bilateral Croatian-French Cogito Hubert Curien project, Leader Vesna Županović, French leader Pavao Mardešić
3. Classifications of Dulac maps and epsilon-neighborhoods, October 16, 2017– January 15, 2019
4. Fractional analog and mixed systems for signal processing, 2017– 2021, HRZZ, collaborator
5. Geometric, Ergodic and Topological Analysis of Low-Dimensional Dynamical Systems, 2015– 2019, HRZZ collaborator
6. Kinetic wealth distribution models and diffusive limit equations, 2010– 2011, bilateral Croatian-Austrian project, collaborator
7. Viscous approximation of quantum Euler-Poisson systems, 2009– 2010, bilateral Croatian-Austrian project, collaborator
8. Nonlinear analysis of differential equations and dynamical systems, 2007– 2013, MZOŠ, collaborator
9. Control of mobile robots and vehicles in unknown and dynamics environments, 2007– 2013, MZOŠ, collaborator
10. Fractional Calculus, Higher Transcedental Functions and Applications,2008– 2009, bilateral Croatian-Macedonian project, collaborator
11. Bifurcations and strange attractors of generalized Lozi maps, University of Zagreb grant
12. Multiplicity of fixed and singular points of dynamical systems and maps, University of Zagreb grant
13. Fractal analysis of Poincaré map, Abelian integrals and normal forms, University of Zagreb grant 2013
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RADDAR mathematics and computer science popularization program 2013-today, leader,
Partners-FER, XV. gimnazija, Croatian Mathematical Society, MNM Marin Getaldić
STEM geniuses project, funded by European Social Fund, 2015-2016, collaboration in writing handbook http://www.stem-genijalci.eu/matematika-informatika