Obiettivo The project concerns one of fundamental problems in theory of dynamical systems, namely non-integrability criterion. The main aim is an exhaustive analysis of the most effective method of proving of non-integrability, namely Morales-Ramis theory, and its development indirections important for integrability theory. At first, we plan to apply this method to various dynamical Hamiltonian system in order to point out difficulties of practical and theoretical nature which appear during its applications. Then we will work out algorithms that allow carrying effectively all steps of Morales-Ramis approach. Next we plan development this method in various directions: adaptation to non - Hamiltionian systems of various kinds, sharpening non - integrability theorems by application of non-homogeneous normal variation alequations, formulation results about partial integrability and super-integrability, working out effective methods of proving real non-in-tegrability by means using appropriate families of particular solutions. As by-product integrability of many systems will be investigated Applicant will obtain a possibility of working under one of the most effective techniques of proving of non-integrability formulated in language of differential Galois theory with a leading specialist in this field. Obtained results and experience will by used in future scientific activity and in preparation of habilitation thesis of applicant Host institution obtain a possibility acquainting with methods and techniques applied in integrability theory by physicists and astronomers, with many interesting examples and results formulated by them. Since Morales. Ramis theory connects integrability with properties of differential Galois groups, this project will stimulate further studies in this branch of mathematics and yield new interpretations. Campo scientifico natural sciencesmathematicsapplied mathematicsdynamical systems Programma(i) FP5-HUMAN POTENTIAL - Programme for research, technological development and demonstration on "Improving the human research potential and the socio-economic knowledge base" (1998-2002) Argomento(i) Data not available Invito a presentare proposte Data not available Meccanismo di finanziamento RGI - Research grants (individual fellowships) Coordinatore INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE - INRIA Contributo UE Nessun dato Indirizzo Route des Lucioles 2004 06902 SOPHIA ANTIPOLIS Francia Mostra sulla mappa Costo totale Nessun dato