We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ z 2 + c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a “Recursive Quadratic Estimate” for the Poincaré series of an infinitely renormalizable map. Sto...

We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ z + c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a “Recursive Quadratic Estimate” for the Poincaré series of an infinitely renormalizable map. Stony...

– A buck converter controlled by naturally-sampled constant frequency pulsewidth modulation in continuous mode of operation is analysed. For a fixed set of converter parameters and varying the dc supply voltage only the buck converter can be driven into chaos through a process of period doublings. A good agreement between simulation and experiments is obtained. Key-words: buck converter , ident...

Contracting the h-deformation of SL(2, R), we construct a new deformation of two dimensional Poincaré algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed...

We analytically study the relationship between the Poincaré map and its one step discretization. Error estimates are established depending basically on the right hand side function of the investigated ODE and the given numerical scheme. Our basic tool is a parametric version of a Newton–Kantorovich type methods. As an application, in a neighborhood of a non-degenerate periodic solution a new ty...

We prove that every reversible Markov semigroup which satisfies a Poincaré inequality matrix-valued for Hermitian d×d matrix valued functions, with the same constant. This generalizes recent results [ABY19, Kat20] establishing such inequalities specific semigroups and consequently yields new concentration inequalities. The short proof follows from spectral theory of generators.

A new mathematical concept of abstract similarity is introduced and illustrated in the space infinite strings on a finite number symbols. The problem chaos presence for Sierpinski fractals, Koch curve, as well Cantor set solved by considering natural map. This accomplished Poincaré, Li-Yorke Devaney chaos, including multi-dimensional cases. Original numerical simula...

Abstract The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation the system results in periodic, quasi-periodic, chaotic and unbounded behavior. An explicit Poincaré map constructed an implicit constraint on switching time. stability fixed points corresponding to period-one solutions By varying parameters, we observed saddle-center pitchfork bifu...

The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincaré map in representation of angular momentum. This has two important implications: we have a paradigm of a true quantum Poincaré map without semiclassical input and we get an entirely new insight into the significance of MQDT. PACS: 05.45.Mt; 33.80.Rv; 03.65.Sq In recent years there has been a rapidly growing ...

In this paper we derive explicit formulas for the normal form coefficients to verify the nondegeneracy of eight codimension two bifurcations of fixed points with one or two critical eigenvalues. These include all strong resonances, as well as the degenerate flip and Neimark-Sacker bifurcations. Applying our results to n-dimensional maps, one avoids the computation of the center manifold, but on...