ON THE MIXING PROPERTIES OF PIECEWISE EXPANDING MAPS UNDER COMPOSITION WITH PERMUTATIONS, II: MAPS OF NON-CONSTANT ORIENTATION

@article{Byott2012ONTM,
  title={ON THE MIXING PROPERTIES OF PIECEWISE EXPANDING MAPS UNDER COMPOSITION WITH PERMUTATIONS, II: MAPS OF NON-CONSTANT ORIENTATION},
  author={Nigel P. Byott and Congping Lin and Yiwei Zhang},
  journal={Stochastics and Dynamics},
  year={2012},
  volume={16},
  pages={1660013}
}
For an integer m ≥ 2, let 𝒫m be the partition of the unit interval I into m equal subintervals, and let ℱm be the class of piecewise linear maps on I with constant slope ±m on each element of 𝒫m. We investigate the effect on mixing properties when f ∈ℱm is composed with the interval exchange map given by a permutation σ ∈ SN interchanging the N subintervals of 𝒫N. This extends the work in a previous paper [N. P. Byott, M. Holland and Y. Zhang, DCDS 33 (2013) 3365–3390], where we considered… 
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References

SHOWING 1-10 OF 54 REFERENCES

On the mixing properties of piecewise expanding maps under composition with permutations

We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal subintervals and $f$ is composed with a permutation of these. The

On iterated maps of the interval

Introduction. Mappings from an interval to itself provide the simplest possible examples of smooth dynamical systems. Such mappings have been widely studied in recent years since they occur in quite

On Entropy and Monotonicity for Real Cubic Maps

Abstract:Consider real cubic maps of the interval onto itself, either with positive or with negative leading coefficient. This paper completes the proof of the “monotonicity conjecture”, which

Entropy in Dimension One

This paper completely classifies which numbers arise as the topological entropy associated to postcritically finite self-maps of the unit interval. Specifically, a positive real number h is the

Fredholm determinant for piecewise linear transformations

We call the number ξ the lower Lyapunov number. We will study Spec^) , the spectrum of P \BV> the restriction of P to the subspace BV of functions with bounded variation. The generating function of P

An inclusion region for the field of values of a doubly stochastic matrix based on its graph

of the complex plane by Lk. This is precisely the region in which complex numbers u + iv satisfy u + Ivl tan (w/k)-< 1. It has been shown [1, 5, 7] that if A = (%) is an n-by-n entry-wise nonnegative

Iterated maps on the interval as dynamical systems

Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic and

Combinatorial Dynamics and Entropy in Dimension One

Preliminaries: general notation graphs, loops and cycles. Interval maps: the Sharkovskii Theorem maps with the prescribed set of periods forcing relation patterns for interval maps antisymmetry of

Sharp polynomial estimates for the decay of correlations

We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young’s estimates on towers

Acceleration of one-dimensional mixing by discontinuous mappings

...