ar X iv : s ol v - in t / 9 80 50 01 v 1 2 M ay 1 99 8 Analytical Study of the Julia Set of a Coupled Generalized Logistic Map

ar X iv : s ol v - in t / 9 80 50 02 v 1 7 M ay 1 99 8 On the Miura and Bäcklund transformations associated with the supersymmetric Gelfand - Dickey bracket

The supersymmetric version of the Miura and Bäcklund transformations associated with the supersymmetric Gelfand-Dickey bracket are investigated from the point of view of the Kupershmidt-Wilson theorem.

ar X iv : c on d - m at / 9 30 50 01 v 1 3 M ay 1 99 3 One - dimensional asymmetrically coupled maps with defects

ar X iv : s ol v - in t / 9 70 50 02 v 1 1 M ay 1 99 7 Rational solutions to d - P IV

We study the rational solutions of the discrete version of Painlevé’s fourth equation (d-PIV). The solutions are generated by applying Schlesinger transformations on the seed solutions −2z and −1/z. After studying the structure of these solutions we are able to write them in a determinantal form that includes an interesting parameter shift that vanishes in the continuous limit.

ar X iv : s ol v - in t / 9 61 00 10 v 2 2 6 M ay 1 99 7 An orthogonal basis for the B N - type Calogero model

We investigate algebraic structure for the BN -type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis.

ar X iv : s ol v - in t / 9 50 60 01 v 1 7 J un 1 99 5 Separation of Variables in the BC - type Gaudin Magnet ∗

The integrable system is introduced based on the Poisson rs-matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The separation of variables is discussed for both classical and quantum case.