We show that dissipative dynamical systems with constant Jacobian allow one to recover numerical values of control parameters under which the system is operating. This is done by performing measurements on self-similar (fractal) structures in phase space. We illustrate parameter recovery...

We generalize the concept of symplectic maps to that of k- symplectic maps: maps whose kth iterates are symplectic. Similarly, k-symmetries and k-integrals are symmetries (resp. integrals) of the kth iterate of the map. It is shown that k-symmetries and k-integrals are related by the...

We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a...

Conolly et al. [Math. Scientist 22 (1997) 83–91] have obtained the transient distribution for a random walk moving on the integers -∞k∞ of the real line. Their analysis is based on a generating function technique. In this paper, an alternative technique is used to derive elegant explicit...

The main goal of this work is the development of the correct methodology of calculation of the Green's function of broken symmetry structures. The two methods were analysed and it was concluded that the direct method with the use of the translational operators is not convenient for the analyses...

A systematic investigation on the complete integrability of the nonautonomous discrete–discrete modified Korteweg–de Vries (ΔΔmKdV) and sine Gordon (ΔΔsG) mappings is presented using Lax pair technique and singularity confinement criteria. We derive conditions on the coefficients of Lax...