Dynamics and Numbers
About this Title
Sergiǐ Kolyada, National Academy of Sciences of Ukraine, Kiev, Ukraine, Martin Möller, Frankfurt University, Frankfurt, Germany, Pieter Moree, Max-Planck Institute for Mathematics, Bonn, Germany and Thomas Ward, Durham University, Durham, United Kingdom, Editors
Publication: Contemporary Mathematics
Publication Year: 2016; Volume 669
ISBNs: 978-1-4704-2020-8 (print); 978-1-4704-3498-4 (online)
This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014.
The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.
Graduate students and research mathematicians interested in number theory, dynamical systems, and ergodic theory.
Table of Contents
- S. Bezuglyi and O. Karpel – Bratteli diagrams: Structure, measures, dynamics
- Alexander Blokh, Lex Oversteegen, Ross Ptacek and Vladlen Timorin – The combinatorial Mandelbrot set as the quotient of the space of geolaminations
- Tomasz Downarowicz, Bartosz Frej and Pierre-Paul Romagnoli – Shearer’s inequality and infimum rule for Shannon entropy and topological entropy
- Alexander Fel’shtyn and Jong Bum Lee – The Nielsen and Reidemeister theories of iterations on infra-solvmanifolds of type $(R)$ and poly-Bieberbach groups
- M. Gröger and T. Jäger – Some remarks on modified power entropy
- Wen Huang and Xiaomin Zhou – Recurrent sets, entropy and independence
- Sergiǐ Kolyada, Michał Misiurewicz and L’ubomír Snoha – Loops of transitive interval maps
- Dominik Kwietniak, Martha Łacka and Piotr Oprocha – A panorama of specification-like properties and their consequences
- Alina Ostafe and Min Sha – Counting dynamical systems over finite fields
- Anke D. Pohl – Symbolic dynamics, automorphic functions, and Selberg zeta functions with unitary representations
- Viktor Schroeder and Steffen Weil – The aperiodic complexities and connections to dimensions and Diophantine approximation
- Igor E. Shparlinski – Dynamical systems of non-algebraic origin: Fixed points and orbit lengths
- Shaun Stevens, Tom Ward and Stefanie Zegowitz – Halving dynamical systems
- Zhaolong Wang and Guohua Zhang – Chaotic behavior of group actions