Let f be a quadratic polynomial which has an irrationally indi erent xed point Let z be a biaccessible point in the Julia set of f Then In the Siegel case the orbit of z must eventually hit the critical point of f In the Cremer case the orbit of z must eventually hit the xed point Siegel polynomials with biaccessible critical point certainly exist but in the Cremer case it is possible that biac...

We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...

Di erent options for block oating point lter implementation are introduced and their e ciency determined. The e ciency is quanti ed by the additional number of operations over those required for xed point operation. Some of the implementations are new. It is shown that they are more e cient than the existing ones. Examples are given in which the processing time per recursion of a block oating p...

This paper presents an algorithm for solving Boolean xed-point equations containing one level of nesting of minimum and maximum xed points. The algorithm assumes that the equations of the inner xed point is of a certain restricted kind and has a worst-case time-and space-complexity that is linear in the size of the equation system. By observing that a range of behavioral relations { in particul...

We deene a value-based modal-calculus, built from rst-order formulas, modalities, and xed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over Crl terms deened by linear process equations. The satisfaction of a temporal formula by a Crl term is translated to the satisfaction of a rst-order formula containing pa...

We consider a perturbed nonlinear system with a xed point that is invariant under all perturbations. Under the assumption that this xed point is locally exponentially stable for the unperturbed system we propose a method for the approximation of the robust domain of attraction, that is, the set of points that are attracted to the xed point under all time-varying perturbations taking values in a...

The automatic conversion of oating point software implementations of algorithms to a equivalent xed point implementation which can be eeciently implemented in an FCCM remains an obstacle in the rapid systems prototyping design ow. Floating point to xed point conversion is tedious, error prone and requires a good knowledge of xed point computer arithmetic. This paper describes a software system ...

We examine the eecient implementation of back prop type algorithms on T0 4], a vector processor with a xed point engine, designed for neural network simulation. A matrix formulation of back prop, Matrix Back Prop 1], has been shown to be very eecient on some RISCs 2]. Using Matrix Back Prop, we achieve an asymptotically optimal performance on T0 (about 0.8 GOPS) for both forward and backward ph...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

When the saddle-center bifurcation occurs in an analytic family of area-preserving maps, rst a parabolic xed point appears at the origin and then this point bi-furcates, creating an elliptic xed point and a hyperbolic one. Separatrices of the hyperbolic xed point form a small loop around the elliptic point. In general the sep-aratrices intersect transversely and the splitting is exponentially s...