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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Intersection theory for ergodic solenoids

Intersection theory for ergodic solenoids

Chapter:
(p.623) Intersection theory for ergodic solenoids
Source:
Frontiers in Complex Dynamics
Author(s):

Vicente Munoz

Ricardo Perez-Marco

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0022

This chapter undertakes a systematic study of the interplay between dynamics and algebraic topology by developing the intersection theory associated to immersed, oriented, and measured solenoids. In a previously published work the concept of k-solenoid has been defined as an abstract laminated space and proved that a solenoid with a transversal measure immersed in a smooth manifold defines a generalized Ruelle–Sullivan current. Considering as object the abstract space with the inmersion provides a more versatile concept than previously considered by other scholars. This chapter intends to study and develop the geometric intersection theory of such objects.

Keywords:   intersection theory, geometric intersection theory, ergodic solenoids, transversal measure, Ruelle–Sullivan current, abstract laminated space

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