Objectif The proposed research includes the following two main directions:(1) Using methods and tools of algebraic geometry and computational algebra, we study the integrability of the nonlinear dynamical systems. We focus on finding the varieties of integrability of dynamical systems with the emphasize on the higher dimensional systems. Our approaches are based on combining symbolic computations with methods of the theory of integrability of dynamical systems. We then study bifurcations of limit cycles and critical periods arising after perturbations of higher dimensional integrable systems of differential equation. Furthermore, we intend to study the problem of isochronicity (which is equivalent to the problem of linearization). (2) We propose to study the global topological linearization, linearization of integral manifold, smooth linearization with the emphasis on the study of the linearization of non-autonomous systems when the nonlinear term is unbounded or linear system does not possess exponential dichotomy (in critical state). Up to now there are few results concerning the linearization Champ scientifique natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Mots‑clés bifurcation linearization stability Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Thème(s) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Appel à propositions H2020-MSCA-IF-2014 Voir d’autres projets de cet appel Régime de financement MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinateur CENTER ZA UPORABNO MATEMATIKO IN TEORETICNO FIZIKO UNIVERZE V MARIBORU Contribution nette de l'UE € 157 287,60 Adresse MLADINSKA ULICA 3 2000 MARIBOR Slovénie Voir sur la carte Région Slovenija Vzhodna Slovenija Podravska Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 157 287,60