Sternberg linearization theorem for skew products

We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older continuous with respect to the base. The normalization theorem mentioned above may be applied to perturbations of skew products and to the study of new persistent properties of attractors.Comment: 17 page

Complex length and persistence of limit cycles in a neighborhood of a hyperbolic polycycle

Complex limit cycle located in a neighborhood of a hyperbolic polycycle can not vanish under a small deformation that preserves the characteristic values of the vertexes of the polycycle. The cycles either change holomorphically under the change of the parameter, or come to the boundary of the fixed neighborhood of the polycycle. The present paper makes these statements rigorous and proves them

Restricted version of the infinitesimal Hilbert 16th problem

The paper deals with an abelian integral of a polynomial 1- form along a family of real ovals of a polynomial (hamiltonian) in two variables (the integral is considered as a function of value of the hamiltonian). We give an explicit upper bound of the number of its zeros (assuming the hamiltonian ultra-Morse of arbitrary degree and ranging in a compact subset in the space of ultra-Morse polynomials of a given degree, and that the form has a smaller degree). This bound depends on the choice of the compact set and is exponential in the fourth power of the degree

Catalytic and mechanistic studies into the epoxidation of styrenes using manganese complexes of structurally similar polyamine ligands

The synthesis and catalytic activity of manganese(ii) complexes of two polyamine ligands is reported which highlights how a small structural change in the ligand affects the overall catalytic behaviour.</p