Pitchfork bifurcation for non-autonomous interval maps

Abstract

In this work, we investigate attracting periodic orbits for non-autonomous discrete dynamical systems with two maps using a new approach. We study some types of bifurcation in these systems. We show that the pitchfork bifurcation plays an important role in the creation of attracting orbits in families of alternating systems with negative Schwarzian derivative and it is central in the geometry of the bifurcation diagrams.

Keywords:

• non-autonomous system
• attracting periodic orbit
• unimodal map
• logistic map
• bimodal map
• pitchfork bifurcation

1991 Mathematics Subject Classification:

• Primary: 37E05
• Secondary: 37E99

Acknowledgements

Emma D'Aniello would like to thank the Department of Mathematics of the Instituto Superior Técnico of Lisbon for its hospitality during her stay, and also the CAMGSD.

Henrique Oliveira would like to thank the Departments of Mathematics of Seconda Universitá degli Studi di Napoli and of Universitá degli Studi di Napoli Federico II for their hospitality during his stay.

Notes

1. [email protected]

Additional information

Notes on contributors

Emma D'Aniello

1