# 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…

## One Citation

### Optimal Mixing Enhancement by Local Perturbation

- PhysicsSIAM Rev.
- 2016

A flexible modeling approach is developed based on the transfer operator of the dynamical system, and the optimal local perturbations can be efficiently computed, at discrete time instants, by standard convex optimization techniques.

## References

SHOWING 1-10 OF 54 REFERENCES

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

- Mathematics
- 2012

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

- Mathematics
- 1988

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

- Mathematics
- 1998

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

- Mathematics
- 2014

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

- Mathematics
- 1990

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

- Mathematics
- 1978

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

- Mathematics
- 1980

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

- Mathematics
- 2000

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

- Mathematics
- 2002

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…