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On Eventually Expanding Maps of the Interval

Title:

On Eventually Expanding Maps of the Interval

GÓRA, PAWEŁ and ESLAMI, PEYMAN (2011) On Eventually Expanding Maps of the Interval. The American Mathematical Monthly, 118 (7). pp. 629-635. ISSN 00029890

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Official URL: http://dx.doi.org/10.4169/amer.math.monthly.118.07...

Abstract

In this paper we conjecture that the piecewise linear map f(x) = px for 0 ≤ x < 1/p, f(x) = sx - s/p for 1/p ≤ x ≤ 1, p > 1, 0 < s < 1, which has an expanding, onto branch and a contracting branch, is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that ⌈− ln(p(1−s)+s)/lns⌉ ≠ ⌈−lnp/lns⌉.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:GÓRA, PAWEŁ and ESLAMI, PEYMAN
Journal or Publication:The American Mathematical Monthly
Date:2011
Digital Object Identifier (DOI):10.4169/amer.math.monthly.118.07.629
ID Code:976827
Deposited By: DANIELLE DENNIE
Deposited On:29 Jan 2013 14:12
Last Modified:18 Jan 2018 17:43

References:

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