where ff = [z‘:w‘],rER and S = i2$<', F=A22-SA12, G = A2,SAU, Ai=[An:A}2\, ~,,ER . Other matrices are compatibly dimensioned. Again it should be noted that the dimension of the partitions in the matrices are not the same as in (1). Equation @I) represents an underdetermined set of (n — m) equations in n unknowns, and thus m entries in each eigenvector corresponding to z-vector can be arbitraril...

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) Hq relevant to the fluctuation spectrum and poles of the order-q power spectrum is proposed. The “partition function” is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A so...

An algorithm is presented for the accurate evaluation of Hankel (or Bessel) transforms of algebraically related kernel functions, defined here as the non-Bessel function portion of the integrand, that is more widely applicable than the standard digital filter methods without enormous increases in computational burden. The algorithm performs the automatic integration of the product of the kernel...

We exhibit explicitly the continued fraction expansion of some algebraic power series over a finite field. also discuss Diophantine equations on ring polynomials, which are intimately related to these series.