The discrete dynamics generated by a continuous map can be represented combinatorially by an appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. In this paper we provide explicit algorithms and computational complexity bounds for computing dynamical structures for the resulting combinatorial multivalued maps. Specifically we focus on the c...

We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coeecients analytic functions. We show that the determinants of these matrices converge to the inver...

The initial value problem for the KdV equation @tu+ u@xu + @ 3 xu = 0; u(x; 0) = (x) establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). It has been known for many years that this map K is continuous [2] , [17] and is proved recently being Lipschitz continuous [23]. In this paper it is shown that the nonlinear map K is in nitely many times Frechet di erentiable from H(R) to C([ T; T ];...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...