Objective This project includes the study of local and nonlocal bifurcations giving rise to strange attractors and homoclinic orbits. In particular, the list of shortened normal forms for bifurcations of equilibria and periodic orbits with three or more characteristic exponents lying on the imaginary axis will be proposed in the case of additional discrete symmetries. Qualitative analysis of the three and four-dimensional (4-D) normal forms will be carried out with special attention paid to detecting Lorenz-like attractors in three dimensions and their multi-dimensional analogues in the four-dimensional case.In a nonlocal situation the automatic control system with an arbitrary feedback function will be studied, together with some coupled maps and heteroclinic contours in 4-D Hamiltonian systems. In all cases homoclinic orbits and strange attractors are expected to occur. The theory of relaxation oscillations will be extended to singularly perturbed differential equations with time delay and to partial differential equations (PDE) of parabolic and hyperbolic types. An asymptotic theory for singularly perturbed PDEs of mixed type and for some bisingular equations will be developed. The problem of the upper estimate of the number of zeros of parameter-dependent abelian integrals is the infinitesimal version of Hilbert's 16th problem. Upper estimates based on new ideas will be obtained. Moreover, the cyclicity of policycles occuring in typical k-parameter families will be estimated through the number of parameters only. Attractors of evolutionary systems will also be studied and their fractal dimension estimated with the dimension of the plane, onto which the attractor may be projected bijectively. The subject of order and chaos in dynamical systems is currently one of the most active areas of research. Modern developments in this field started with computers. Applications of particular interest are to be found in celestial mechanics and, in particular, in the distribution of asteroids and the motion of satellites. For various classes of dynamical systems the investigation of instability of trajectories will be presented. The frequency-domain estimates of bifurcational values of parameters corresponding to loss of stability in homoclinic orbits will be studied. Topological, arithmetic and spectral properties of adic systems (essentially substitutions) will be investigated. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Topic(s) 21 - Mathematics Call for proposal Data not available Funding Scheme Data not available Coordinator Rijksuniversiteit Utrecht EU contribution No data Address Budapestlaan 6 3508 TA Utrecht Netherlands See on map Total cost No data Participants (9) Sort alphabetically Sort by EU Contribution Expand all Collapse all Facultés Universitaires Notre-Dame de la Paix Belgium EU contribution No data Address 5000 Namur See on map Total cost No data Institute for Applied Mathematics and Cybernetics Russia EU contribution No data Address 603005 Nizhny Novgorod See on map Total cost No data Moscow State University M.V. Lomonosov Russia EU contribution No data Address 119899 Moscow See on map Total cost No data Moscow State University M.V. Lomonosov Russia EU contribution No data Address 119899 Moscow See on map Total cost No data Russian Academy of Sciences Russia EU contribution No data Address 191011 St. Petersburg See on map Total cost No data St. Petersburg State University Russia EU contribution No data Address 198904 St. Petersburg See on map Total cost No data St. Petersburg State University Russia EU contribution No data Address 198004 Petrodvorets - St. Petersburg See on map Total cost No data Université de la Méditerranée - Marseille II France EU contribution No data Address 13288 Marseille See on map Total cost No data Volga State Academy of Water Transportation Russia EU contribution No data Address 603600 Nizhny Novgorod See on map Total cost No data
