The chaos bound in the near-horizon regions has been studied through expansions of metric functions on horizon. In this paper, we investigate region and at a certain distance from horizon charged Kiselev black hole. value Lyapunov exponent is accurately calculated by Jacobian matrix. angular momentum particle around hole affects not only exponent, but also position equilibrium orbit. This gradu...

We study the stability of linear fractional order maps. show that in stable region, evolution is described by Mittag-Leffler functions and a well-defined effective Lyapunov exponent can be obtained these cases. For one-dimensional systems, this related to corresponding differential equation. A equivalent map [Formula: see text] for where parameter text]. coupled maps, we obtain ‘normal modes’ r...

The influence of the angular momentum particle on Lyapunov exponent has been studied. In this paper, we investigate influences charge and a around non-extremal extremal Reissner-Nordstr\"om black holes with scalar hair exponent, find spatial regions where chaos bound is violated for certain values holes' parameters. gotten by calculating eigenvalue Jacobian matrix in phase space. violation occu...

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the ...

For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems consider are partially hyperbolic one-dimensional central direction for which there positive whose Lyapunov exponent is negative, zero, or positive. We zero and the topological set points zero. This provides restricted vari...

A construction approach for the 3-band tight wavelet frames by factorization of paraunitarymatrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the paramete...

We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and ...

Smoothness and symmetry are two important properties of a refinable function. It is known that the Sobolev smoothness exponent of a refinable function can be estimated by computing the spectral radius of a certain finite matrix which is generated from a mask. However, the increase of dimension and the support of a mask tremendously increases the size of the matrix and therefore makes the comput...

We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in ~ O(n2+ ) time, where satisfies the equation !(1; ; 1) = 1 + 2 and !(1; ; 1) is the...