## Taiwanese Journal of Mathematics

### AN IMPROVED STABILITY CRITERION WITH APPLICATION TO THE ARNEODO-COULLET-TRESSER MAP

#### Abstract

We give a criterion of discrete stability for polynomials of degree $n \leq 4$ in terms of polynomial inequalities which contain linear inequalities and only one inequality of degree $n-1$. The result then applies to study stability regions for fixed points of the Arneodo-Coullet-Tresser maps.

#### Article information

Source
Taiwanese J. Math., Volume 11, Number 5 (2007), 1369-1382.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500404870

Digital Object Identifier
doi:10.11650/twjm/1500404870

Mathematical Reviews number (MathSciNet)
MR2368655

Zentralblatt MATH identifier
1135.37305

Subjects
Primary: 37C75: Stability theory 37G10: Bifurcations of singular points

#### Citation

Du, B.-S.; Hsiau, S.-R.; Li, M.-C.; Malkin, M. AN IMPROVED STABILITY CRITERION WITH APPLICATION TO THE ARNEODO-COULLET-TRESSER MAP. Taiwanese J. Math. 11 (2007), no. 5, 1369--1382. doi:10.11650/twjm/1500404870. https://projecteuclid.org/euclid.twjm/1500404870