Phase Description Method to Invariant Densities in I-D Difference Systems

Approximating invariant densities of metastable systems

We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a convex combination of the two initial...

Corn grain yield responses to tillage systems and plant densities

Mixing Invariant Densities

| For many chaotic systems there appears to be a single asymptotic distribution describing the frequency with which almost all trajectories visit diierent regions of state space. Such a distribution is commonly called the \physical" invariant measure or \natural" invariant measure of the system. Consider the evolution of a cluster of initial conditions under the action of the system. This clust...

Regularity of Invariant Densities for 1d-systems with Random Switching

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Difference equations and n-D discrete systems

Abstract Discrete systems are often described by difference equations. With some attributes of initial state type, a difference equation defines a system, i.e. a set of (input,output) pairs. For systems defined by linear difference equations (with constant or variable coefficients) on arbitrary sets A ⊂ Z sufficient conditions of their stability are formulated. It is also shown that these condi...