Periodic structure of alternating continuous interval maps

Abstract

Given two continuous interval maps f and g, we study the periodic structure for the set of sequences generated by f and g by the rule . It is shown that this structure is intimately related to that of Sharkovsky's Theorem, although some differences appear with the periods that are coprime with 2.

Keywords:

• Discrete dynamical system
• Set of periods
• Sharkovsky's Theorem
• Continuous interval maps
• Forcings

Keywords:

• Primary: 37E05
• Secondary: 37B20
• 37E99

Acknowledgements

We want to thank Professor Saber Elaydi for his comments concerning the characterization of periods of via geometric r-cycles.

Additional information

Notes on contributors

Jose S. Cánovas

This paper has been partially supported by the Grant FS 00684/PI/04 from Fundación Séneca (Comunidad Autónoma de la Región de Murcia, Spain) and Grant MTM 2005-03868 from Ministerio de Educación y Ciencia, Spain.

Antonio Linero

This paper has been partially supported by the Grant FS 00684/PI/04 from Fundación Sóneca (Comunidad Autónoma de la Región de Murcia, Spain) and Grant MTM 2005-03868 from Ministerio de Educación y Ciencia, Spain.