Lattice Structures for Attractors II

Lattice Structures for Attractors II

The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics...

Lattice Structures for Attractors I

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a f...

Multiscale autoregressive processes. II. Lattice structures for whitening and modeling

Random Attractors for Stochastic Retarded Lattice Dynamical Systems

and Applied Analysis 3 It is worth mentioning that in the absence of the white noise, the existence of a global attractor for 1.3 1.4 was established in 40 . The main contribution of this paper is to extend the method of tail estimates to stochastic retarded LDSs and prove the existence of a random attractor for the infinite dimensional random dynamical system generated by stochastic retarded L...

Lattice Structures for Quantum Channels

We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra Mn might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is quite intricate, it admits a simple, lattice structure representation.