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.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
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Coordinator
3508 TA Utrecht
Netherlands
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.