Operatori pomaka, statistički zakoni i beskonačno-dimenzionalni dinamički sustavi 

HRZZ projekt 2020-2023 (IP-2019-04-1239)

                      

 Sažetak:

Glavni cilj ovog projekta je ostvariti značajne doprinose u nekoliko različitih područja suvremene teorije dinamičkih sustava, kao i u usko povezanim područjima poput teorije vjerojatnosti i numeričke matematike. Problemi s kojima se planiramo baviti su teorijske i primijenjene prirode te su značajni ne samo za naša područja stručnosti, već i za druge discipline poput statističke fizike, matematičke statistike, teorije kontrole i inženjerstva. Naše istraživačke aktivnosti će se fokusirati na unapređenju i daljnjem razvoju nedavnih važnih rezultata članova našeg tima, koji su objavaljeni u vodećim međunarodnim časopisima. Naglašavamo da je tijekom razdoblja 2014.-2019. naš tim publicirao 19 Q1 i 19 Q2 članaka. Najnoviji rezultati uključuju: razne granične teoreme za slučajne dinamičke sustave, uključujući prvu verziju lokalnog centralnog graničnog teorema u ovom kontekstu (D. Dragičević); prve rezultate posvećene glatkoj linearizaciji neautonomnih hiperboličnih dinamičkih sustava (D. Dragičević); razne spektralne karakterizacije hiperboličnosti neautonomnih dinamičkih sustava (D. Dragičević); nove funkcionalne granične teoreme za slabo zavisne slučajne procese (D. Krizmanić); nove algoritme pretraživanja (B. Crnković). Osim znanstvenog napretka, naš je cilj nastaviti postojeće i inicirati nove produktivne suradnje s više vodećih međunarodnih sveučilišta i eminentnih stručnjaka u našim područjima istraživanja. To će ne samo učiniti naš istraživački tim vidljivijim, nego će i poboljšati međunarodnu prepoznatljivost Odjela za matematiku Sveučilišta u Rijeci. Štoviše, zapošljavanjem jednog doktoranda i jednog postdoktoranda planiramo privući mlade perspektivne matematičare te im pružiti poticajno istraživačko okruženje i mogućnost rada pod vodstvom energičnih iskusnih istraživača. To će također doprinijeti jačanju našeg istraživačkog tima.

 Voditelj projekta: izv. prof. dr. sc. Davor Dragičević (Fakultet za matematiku Sveučilišta u Rijeci) 

 Istraživački tim:  
izv. prof. dr. sc. Bojan Crnković (Fakultet za matematiku Sveučilišta u Rijeci)
izv. prof. dr. sc. Danijel Krizmanić (Fakultet za matematiku Sveučilišta u Rijeci)
dr. sc. Lokesh Singh (Fakultet za matematiku Sveučilišta u Rijeci)
Mila Zovko (Fakultet prirodoslovno-matematičkih i odgojnih znanosti Sveučilišta u Mostaru)

 Objavljeni radovi:
  1. D. Dragičević, Barbashin-type conditions for exponential stability of linear cocycles, Monatshefte für Mathematik 19 (2020), 813-826.
  2. L. Backes, D. Dragičević, Quasi-shadowing for partially hyperbolic dynamics on Banach spaces, Journal of Mathematical Analysis and Applications 492 (2020), 124445
  3. S. Ivić, B. Crnković, H. Arbabi, S. Loire, P. Clary, I. Mezić, Search strategy in a complex and dynamic environment: the MH370 case, Scientific Reports 10, 19640 (2020) [link]
  4. D. Dragičević, Y. Hafouta, Limit theorems for random expanding or Anosov dynamical systems and vector-valued observables, Annales Henri Poincare 21 (2020), 3869-3917.
  5. D. Dragičević, N. Jurčević Peček, N. Lupa, Admissibility and general dichotomies for evolution families, Electronic Journal of Qualitative Theory of Differential Equations 2020 (2020), 58, 19pp.
  6. L. Backes, D. Dragičević, Shadowing for infinite dimensional dynamics and exponential trichotomies, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 151 (2021), 863-884.
  7. D. Dragičević, Hyers-Ulam stability for nonautonomous semilinear dynamics on bounded intervals, Mediterranean journal of mathematics 18 (2021), 9pp.
  8. D. Dragičević, M. Pituk, Shadowing for nonautonomous difference equations with infinite delay, Applied Mathematics Letters 120 (2021), 107284, 8pp.
  9. L. Backes, D. Dragičević, A general approach to nonautonomous shadowing for nonlinear dynamics, Bulletin des Sciences Mathematiques 170 (2021), 102996, 30pp.
  10. D. Dragičević, Hyers-Ulam stability for a class of perturbed Hill's equations, Results in Mathematics 76 (2021), 11pp.
  11. L. Backes, D. Dragičević, K. J. Palmer, Linearization and Holder Continuity for Nonautonomous Systems, Journal of Differential Equations 297 (2021), 536-574.
  12. L. Singh, D. Bahuguna, Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate, Axioms 10 (2021), 14pp.
  13. D. Dragičević, Y. Hafouta, Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations, Thermodynamic Formalism-CIRM Jean Morlet Chair Fall 2019, Lecture Notes in Mathematics, vol. 2290, 177-204.
  14. L. Backes, D. Dragičević, On the spectral radius of compact operator cocycles, Stochastics and Dynamics 21 (2021), 2150026, 16pp.
  15. L. Backes, D. Dragičević, Hyers-Ulam stability for hyperbolic random dynamics, Fundamenta mathematicae 255 (2021), 69-90.
  16. D. Dragičević, On the Hyers-Ulam stability of certain nonautonomous and nonlinear difference equations, Aequationes Mathematicae 95 (2021), 829-840.
  17. D. Dragičević, Y. Hafouta, Almost sure invariance principle for random dynamical systems via Gouezel's approach, Nonlinearity 34 (2021), 6773-6798.
  18. D. Krizmanić, Maxima of linear processes with heavy-tailed innovations and random coefficients, Journal of Time Series Analysis 43 (2022), 238-262.
  19. D. Krizmanić, A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations, Brazilian Journal of Probability and Statistics 36 (2022), 138-156.
  20. D. Dragičević, A. L. Sasu, B. Sasu, On Stability of Discrete Dynamical Systems - From Global Methods to Ergodic Theory Approaches, Journal of Dynamics and Differential Equations 34 (2022), 1107-1137.
  21. D. Dragičević, A. L. Sasu, B. Sasu, Input-Output Criteria for Stability and Expansiveness of Dynamical Systems, Applied Mathematics and Computation 414 (2022), 126574, 22pp.
  22. L. Backes, D. Dragičević, L. Singh, Shadowing for nonautonomous and nonlinear dynamics with impulses, Monatshefte für Mathematik 198 (2022), 485-502.
  23. D. Dragičević, Global smooth linearization of nonautonomous contractions on Banach spaces, Electronic Journal of Qualitative Theory of Differential Equations (2022), 19pp.
  24. D. Dragičević, W. Zhang, L. Zhou, Admissibility and nonuniform exponential dichotomies, Journal of Differential Equations 326 (2022), 201-226.
  25. D. Dragičević, A. L. Sasu, B. Sasu, On Polynomial Dichotomies of Discrete Nonautonomous Systems on the Half-Line, Carpathian Journal of Mathematics 38 (2022), 663-680.
  26. S. Ivić, A. Sikirica, B. Crnković, Constrained multi-agent ergodic area surveying control based on finite element approximation of the potential field, Engineering applications of artificial intelligence 116 (2022), 105441, 15.
  27. L. Backes, D. Dragičević, A generalized Grobman-Hartman theorem for nonautonomous dynamics, Collectanea Mathematica 73 (2022), 411-431.
  28. D. Dragičević, A. L. Sasu, B. Sasu, L. Singh, Nonuniform Input-Output Criteria for Exponential Expansiveness of Discrete Dynamical Systems and Applications, Journal of Mathematical Analysis and Applications 515 (2022), 126436.
  29. L. Backes, D. Dragičević, M. Pituk, L. Singh, Weighted shadowing for delay differential equations, Archiv der Mathematik 119 (2022), 539-552.
  30. D. Dragičević, A. L. Sasu, B. Sasu, Admissibility and Polynomial Dichotomy of Discrete Nonautonomous Systems, Carpathian Journal of Mathematics 38 (2022), 737-762.
  31. D. Krizmanić, Joint functional convergence of partial sums and maxima for moving averages with weakly dependent heavy-tailed innovations and random coefficients, ALEA Latin American Journal of Probability and Mathematical Statistics 20 (2023), 1247-1270.
  32. D. Krizmanić, A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations, Lithuanian Mathematical Journal 63 (2023), 305-336. 

 Radovi prihvaćeni za objavljivanje:
  1. D. Dragičević, J. Sedro, Statistical stability and linear response for random hyperbolic systems, Ergodic Theory and Dynamical Systems
  2. D. Dragičević, On the robustness property of nonuniform exponential dichotomies, Proceedings of the ICDEA 2021 - Advances in Discrete Dynamical Systems, Difference Equations and Applications, Springer Proceedings in Mathematics & Statistics
  3. L. Backes, D. Dragičević, On the linearization of infinite-dimensional random dynamical systems, Mathematische Nachrichten
  4. S. Ivić, B. Crnković, L. Grbčić, L. Matleković, Multi-UAV trajectory planning for 3D visual inspection of complex structures, Automation in Construction 147 (2023), 104709
  5. D. Dragičević, N. Jurčević Peček, Hyers-Ulam-Rassias stability for nonautonomous dynamics, Rocky Mountain Journal of Mathematics
  6. L. Backes, D. Dragičević, Multiscale linearization of nonautonomous dynamics, Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  7. D. Dragičević, Y. Hafouta, J. Sedro, A vector-valued almost sure invariance principle for random expanding on average cocycles, Journal of Statistical Physics
  8. D. Dragičević, P. Giulietti, J. Sedro, Quenched linear response for smooth expanding on average cocycles, Communications in Mathematical Physics
  9. L. Backes, D. Dragičević, M. Pituk, M. Onitsuka, Conditional Lipschitz shadowing for ordinary differential equations, Journal of Dynamics and Differential Equations 

 Izlaganja na konferencijama:
  1. D. Krizmanić, Joint functional convergence of partial sum and maxima processes, 8th European Congress of Mathematics, Portorož, Slovenija, 20. - 26. lipnja 2021.
  2. D. Krizmanić, On joint weak convergence of partial sum and maxima processes, 7th Croatian Mathematical Congress, Split, Hrvatska, 15. - 18. lipnja 2022.
  3. D. Krizmanić, Functional convergence of maxima of linear processes with heavy-tailed innovations and random coefficients, 13th International Conference on Extreme Value Analysis, Milano, Italija, 26. - 30. lipnja 2023.
  4. D. Krizmanić, Functional convergence of maxima of linear processes with heavy-tailed innovations and random coefficients, 43rd Conference on Stochastic Processes and their Applications - SPA 2023, Lisabon, Portugal, 24. - 28. srpnja 2023. 

 Gostujući znanstvenici: