We consider a family of chaotic skew tent maps. The skew tent map is a two-parameter, piecewise-linear, weakly-unimodal, map of the interval Fa;b. We show that Fa;b is Markov for a dense set of parameters in the chaotic region, and we exactly nd the probability density function (pdf), for any of these maps. It is well known, [1], that when a sequence of transformations has a uniform limit F , a...

The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In particular it is not known whether the topological closure of such graphs is typically a filled-in set, i.e. consist of a single interval on every fibre, or n...

In this note we consider continuous-time systems ẋ(t) = A(t)x(t) + B(t)u(t) as well as discrete-time systems x(t + 1) = A(t)x(t) + B(t)u(t) whose coefficient matrices A and B are not exactly known. More precisely, all that is known about the systems is their nonzero pattern, i.e., the locations of the nonzero entries in the coefficient matrices. We characterize the patterns that guarantee contr...

This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partitionbased invariance controller using the information recorded during the computation. In contrast with Lyapunov-based control methods, this method does not require the subsystems t...

We propose a principled way to construct an internal representation of the temporal stimulus history leading up to the present moment. A set of leaky integrators performs a Laplace transform on the stimulus function, and a linear operator approximates the inversion of the Laplace transform. The result is a representation of stimulus history that retains information about the temporal sequence o...

The Invariant Maximal Clique Theorem asserts that every graph on Q[0,n] with a specific invariance condition has a maximal clique with another specific invariance condition. Here Q[0,n] consists of the rationals in the interval [0,n]. The invariance conditions are all given by equivalence relations involving only < on [0,n] and the distinguished elements 1,...,n. We prove the Invariant Maximal ...

The Invariant Maximal Clique Theorem asserts that every graph on Q[0,n] with a specific invariance condition has a maximal clique with another specific invariance condition. Here Q[0,n] consists of the rationals in the interval [0,n]. The invariance conditions are all given by equivalence relations involving only < on [0,n] and the distinguished elements 1,...,n. We prove the Invariant Maximal ...

Keller [9] introduced families of W–shaped maps that can have a great variety of behavior. As a family approaches a limit W map, he observed behavior that was either described by a probabilty density function (pdf) or by a singular point measure. Based on this, Keller conjectured that instability of the absolutely continuous invariant measure (acim) can result only from the existence of small i...

let s be a locally compact foundation semigroup with identity and                          be its semigroup algebra. let x be a weak*-closed left translation invariant subspace of    in this paper, we prove that  x  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. we also prove that a foundation semigroup with identity s is left amenab...

0. Introduction. This paper extends some results from [1] and applies them to certain transformations of the unit interval. §§2-4 are concerned with symbolic dynamics and §§5-6 are concerned with their application to the proof of our main theorem which states sufficient conditions for a piecewise continuous transformation of the unit interval to be conjugate to a (uniformly) piecewise linear tr...