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- ДокументMoyal and Rankin-Cohen deformations of algebras(2018) Volodymyr LyubashenkoIt is proven that Rankin-Cohen brackets form an associativedeformation of the algebra of polynomials whose coeffcients are holomorphicfunctions on the upper half-plane.
- ДокументA calculation of periodic data of surface diffeomorphisms with one saddle orbit.(2018) Олена В'ячеславівна Ноздрінова, Ольга Віталіївна ПочинкаIn the paper it is proved that any orientable surface admits an orientation-preserving diffeomorphism with one saddle orbit. It distinguishes in principle the considered class of systems from source-sink diffeomorphisms existing only on the sphere. It is shown that diffeomorphisms with one saddle orbit of a positive type on any surface have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established. Namely, formulas are found expressing the periods of the sources through the periods of the sink and the saddle.
- ДокументBypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function(2018) Claire DavidIn the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by[{mathcal W}(x)= sum_{n=0}^{+infty} lambda^n,cos left ( 2, pi,N_b^n,x right),]where $lambda$ and $N_b$ are two real numbers such that $0 1$, using a sequence a graphs that approximate the studied one.