Abstract
Consider a once differentiable one-parameter family of unimodal maps as in the preceding section. We assume for definiteness that the parameter varies in [0,1] and for simplicity we also assume the maps fμ are symmetric functions. If f0 (1) = 0 and f1 = −1, then all maximal admissible itineraries A with \({\rm RC} \leq \underline{{\rm A}} \leq {\rm RL}^{{\infty}}\) occur as the kneading sequence of one of the fμ's. In particular, many non-periodic kneading sequences can occur, and the discussion of Part II has shown that in some cases one has sensitive dependence on initial conditions, while in other situations one finds an absolutely continuous ergodic invariant measure.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Birkhäuser Boston
About this chapter
Cite this chapter
Collet, P., Eckmann, JP. (2009). Abundance of Aperiodic Behavior. In: Iterated Maps on the Interval as Dynamical Systems. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4927-2_17
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4927-2_17
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4930-2
Online ISBN: 978-0-8176-4927-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)