---
abstract: 'We propose a method to identify and to locate "repellers” in quasi-periodically forced logistic map (QPLM), using a kind of Morse decomposition of nested attracting invariant sets. In order to obtain the invariant sets, we use an auxiliary 1+2-dimensional skew-product map system describing the evolution of a line segment in the phase space of QPLM. With this method, detailed structure of repellers can be visualized, and the emergence of a repeller in QPLM can be detected as an easily observable bifurcation in the auxiliary system. In addition to the method to detect the repellers, we propose a new numerical method for distinguishing a strange non-chaotic attractor (SNA) from a smooth torus attractor, using a correspondence between SNAs in QPLM and attractors with riddled basin in the auxiliary system.'
author:
- Tsuyoshi Chawanya
- Takafumi Sakai
date: 3 March 2014
title: 'On repellers in quasi-periodically forced logistic map system'
---

> The topological structure of invariant sets as well as its variation (bifurcation) is one of the most basic and essential issues for understanding the behavior of a dynamical system. However, it is sometimes not easy to obtain invariant sets in non-autonomous systems, and that might make our understanding 