**Contemporary Mathematics**

Volume: 678;
2016;
316 pp;
Softcover

MSC: Primary 37; 01;

**Print ISBN: 978-1-4704-2299-8
Product Code: CONM/678**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-1-4704-3589-9
Product Code: CONM/678.E**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

# Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby

Share this page *Edited by *
*Joseph Auslander; Aimee Johnson; Cesar E. Silva*

This volume contains the proceedings of three
conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby
Centennial Conference, held from October 30–31, 2010, at Bryn Mawr
College; the Williams Ergodic Theory Conference, held from July 27–29,
2012, at Williams College; and the AMS Special Session on Ergodic
Theory and Symbolic Dynamics, held from January 17–18, 2014, in
Baltimore, MD.

This volume contains articles covering a variety of topics in
measurable, symbolic and complex dynamics. It also includes a survey
article on the life and work of John Oxtoby, providing a source of
information about the many ways Oxtoby's work influenced mathematical
thought in this and other fields.

#### Readership

Graduate students and research mathematicians interested in ergodic theory and topological dynamics.

# Table of Contents

## Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby

- Cover 11
- Title page 44
- Contents 66
- Preface 88
- Conjugacy in the Cantor set automorphism group 1818
- The mathematical work of John C. Oxtoby 6060
- The Cech cohomology and the spectrum for 1-dimensional tiling systems 7070
- Markov diagrams for some non-Markovian systems 9090
- Contractive spaces and relatively contractive maps 120120
- Mandelpinski structures in the parameter planes of rational maps 150150
- Substitutions and Möbius disjointness 168168
- Subshifts with slowly growing numbers of follower sets 192192
- Haar measures and Hausdorff dimensions of 𝑝-adic Julia sets 204204
- Lebesgue measure theoretic dynamics of rational maps 214214
- The inverse problem for canonically bounded rank-one transformations 236236
- Higher dimensional shift spaces with shear 248248
- 1. Background Definitions 248248
- 2. Shift Spaces with Shear: Definitions and Examples 249249
- 3. Generalized Shift Products 252252
- 4. \mb𝑍^{𝑑-1}-Shear in \mb𝑍^{𝑑} Shift Spaces 253253
- 5. \mb𝑍^{𝑑-1}-Shear in \mb𝑍^{𝑑} Shifts of Finite Type 257257
- 6. \mb𝑍^{𝑑-1}-Shear in \mb𝑍^{𝑑} Sofic Shifts 259259
- 7. Future Research Questions 259259
- References 260260

- Hereditary subshifts whose simplex of invariant measures is Poulsen 262262
- Substitutions, symbolic codings, and discrepancy 272272
- Nearly continuous even Kakutani equivalence of nearly continuously rank-one transformations 294294
- Dynamics of self-similar interval exchange transformations on three intervals 314314
- Back Cover 336336