Thermodynamic formalism for interval maps: inducing schemes

Abstract

This survey paper concerns inducing schemes in the context of interval maps. We explain how the study of these induced systems allows for the fine description of not only the thermodynamic formalism for certain multimodal maps, but also its multifractal structure.

Keywords:

• equilibrium states
• thermodynamic formalism
• multimodal maps
• multifractal analysis

Acknowledgements

The authors would like to thank H. Bruin, K. Gelfert, L. Olsen, I. Petrykiewicz, J. Rivera-Letelier and the referee for their useful comments. GI was partially supported by the Center of Dynamical Systems and Related Fields código ACT1103 and by Proyecto Fondecyt 111004.

Notes

1. By part (3) of the definition of the class , the topological attractor of a map is always the whole of I.

2. We are grateful to J. Rivera-Letelier for pointing this out to us.