For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We estab...

The work focuses attention on strange but nonchaotic behaviour of dynamic systems as a relatively new phenomenon distinct from the usual strange chaotic one. Several characterization techniques associated with Poincare sections, Lyapunov exponents, capacity and information dimensions are used. It is shown that based on a single time series it is virtually impossible to distinguish between stran...

Poincare polinomials of hyperbolic Lie algebras, which are given by HA2 and HA3 in the Kac’s notation, are calculated explicitly. The results show that there is a significant form for hyperbolic Poincare polinomials. Their explicit forms tend to be seen as the ratio of a properly chosen finite Poincare polinomial and a polinomial of finite degree. To this end, by choosing the Poincare polinomia...

BACKGROUND Poincare plots are commonly used to study the nonlinear behavior of physiologic signals. The aim of this study is to evaluate the Poincare plot indices of human heart rate signals during meditation. METHODS For this purpose, heart rate time series of eight Chi meditators available in Physionet database were used. Poincare plots with lags of 1 and 6 were constructed, and the ratio o...

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of fractional variable order Riemann–Liouville type. issues stability and convergence are considered. Test examples given to substantiate theoretical results. Using Runge rule, results compared explicit scheme. Phase trajectories oscillograms oscillator type constructed, chaotic modes detected ...

The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations o...

We explore the chaotic behavior of particle motion in a black hole with quasi-topological electromagnetism. The chaos bound is found to be violated higher order expansion metric function and electric potential near horizon. draw Poincare sections corresponding non-violated cases, respectively. Then we study relationship between maximal Lyapunov exponent \lambda_s defined by static equilibrium g...

Results on the dynamics of the planar pendulum with parametric vertical timeperiodic forcing are reviewed and extended. Numerical methods are employed to study the various dynamical features of the system about its equilibrium positions. Furthermore, the dynamics of the system far from its equilibrium points is systematically investigated by using phase portraits and Poincare sections. The attr...

We do a study of the real representations of the Poincare group, motivated by the following: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity...