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Sunday, July 26, 2020 | History

2 edition of Zero-entropy automorphisms of a compact abelian group found in the catalog.

Zero-entropy automorphisms of a compact abelian group

Terrance Lee Seethoff

# Zero-entropy automorphisms of a compact abelian group

## by Terrance Lee Seethoff

Published .
Written in English

Subjects:
• Ergodic theory.,
• Topological groups.

• Edition Notes

The Physical Object ID Numbers Statement by Terrance Lee Seethoff. Pagination 67 leaves, bound ; Number of Pages 67 Open Library OL15108034M

The abelian complexity of inﬁnite words and the Frobenius problem. Ian Kaye and Narad Rampersad*, University of Winnipeg () PM () Abelian subshifts. Svetlana Puzynina, Saint Petersburg State University, Russia () PM () On non-repetitive complexity of Arnoux-Rauzy words. Kateˇrina Medkov´a, Edita Pelantov´a,File Size: 1MB. Debmalya Sain.. Source: Annals of Functional Analysis, Advance publication, 9 pages. Abstract: In this paper we completely characterize the norm attainment set of a bounded linear operator between Hilbert spaces. In fact, we obtain two different characterizations of the norm attainment set of a bounded linear operator between Hilbert spaces.

The abelian complexity of infinite words and the Frobenius problem. Ian Kaye, University of Winnipeg Narad Rampersad*, University of Winnipeg () p.m. Abelian subshifts. Svetlana Puzynina*, Saint Petersburg State University, Russia () p.m. On non-repetitive complexity of Arnoux-Rauzy words.   Automorphisms of zero entropy dynamical systems. Van Cyr*, Bucknell University Bryna Kra, Northwestern University John Franks, Northwestern University () a.m. Specification and Markov properties in shift spaces. Vaughn Climenhaga*, University of Houston () a.m.

A RANDOM WALK DRIVEN BY AN IRRATIONAL ROTATION 3 (c) up (a) 1 1 i i 4 4 iv iv 2 2 ii ii 5 5 v vi v 3 3 iii iii (b) 1 1 1 Figure 1. (a) The in nite staircase St; (b) The translation surface St 0 it covers; (c) St 0 is a punctured torus T is ergodic and measure preserving [CK]. But . We introduce a general result relating “short averages” of a multiplicative function to “long averages” which are well understood. This result has several consequences. First, for the Möbius function we show that there are cancellations in the sum of $\mu(n)$ in almost all intervals of the form $[x, x + \psi(x)]$ with $\psi(x) \rightarrow \infty$ arbitrarily slowly.

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### Zero-entropy automorphisms of a compact abelian group by Terrance Lee Seethoff Download PDF EPUB FB2

Although the study of dynamical systems is mainly concerned with single trans­ formations and one-parameter flows (i. with actions of Z, N, JR, or JR+), er­ godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with.

An irreducible algebraic ℤ d -actionα on a compact abelian group X is a ℤd -action by automorphisms of X such that every closed, α-invariant subgroup Y⊊X is : Siddhartha Bhattacharya.

Some of these rigidity properties are inherited by certain abelian subgroups of these groups, but the very special nature of the actions involved does not allow any general conjectures about actions of multi-dimensional abelian groups.

Beyond commuting group rotations, commuting toral automorphisms and certain other algebraic examples (cf. [ Search within book. Front Matter. Pages i-xviii. PDF. CHAPTER I Group actions by automorphisms of compact groups. Zero-entropy automorphisms of a compact abelian group book Schmidt.

Pages CHAPTER II $$\mathbb{Z}^{d}$$-actions on compact abelian groups. Klaus Schmidt. Pages CHAPTER III Expansive automorphisms of compact groups.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new.

Group actions by automorphisms of compact groups --Ch. Z[superscript d]-actions on compact abelian groups --Ch. III. Expansive automorphisms of compact groups --Ch. Periodic points --Ch.

Entropy --Ch. Positive entropy --Ch. VII. Zero entropy --Ch. VIII. Mixing --Ch. Rigidity. Series Title. Groups of Markov type.- II.?d-actions on compact abelian groups.- 5. The dual module.- 6. The dynamical system defined by a Noetherian module.- 7.

The dynamical system defined by a point.- 8. The dynamical system defined by a prime ideal.- III. Expansive automorphisms of compact groups.- 9.

Expansive automorphisms of compact connected. A connected compact abelian group K belongs to E compact abelian group K ∈ E 0 is totally disconnected by Theorem B(b). In contrast with this, the next example shows that E 0 may contain non-abelian compact connected groups: Example Let K = S O 3 (R).Cited by: 3.

book reviews automorphisms of compact abelian groups are isomorphic to Bernoulli shifts if they are mixing, and they are therefore classiﬁed by their entropy, which is easy to "1,thesituationismorecomplicated,asillustratedbythefollowing example due to Ledrappier [2]. Let A be a compact abelian group, and let X A denote.

Abstract: For mixing $\mathbb Z^d$-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure.

in d commuting variables, and M be an Ra-module. Then the dual group X M of M is compact, and multiplication on M by each of the d variables corresponds to an action a M of 7/d by automorphisms of Xu. Every action of 7/d by automorphisms of a compact abelian group arises this way. Iffe R d, our main formula shows that the topological entropy of.

Dynamical Systems of Algebraic Origin by Klaus Schmidt,available at Book Depository with free delivery worldwide. A group G is Hamiltonian if and only if G ≅ Q 8 × B × D, where Q 8 is the quaternion group of order 8, B is a Boolean group and D is a torsion abelian group with all its elements of odd order.

In other words, G ≅ Q 8 × T, where T is an arbitrary torsion abelian group such that T 2 = T [2] is of exponent ≤2. The next definition Author: W.

Xi, M. Shlossberg, D. Toller. FIFTY YEARS OF ENTROPY IN DYNAMICS: – ANATOLE KATOK PREFACE The zero entropy case of both the Ornstein theory and the monotone or Haar measure for an automorphism of a general compact abelian group, or specially constructed, as the Parry measure for a transitiv etopologicalMarkov.

Let X be a compact Kaehler manifold. Let G be a group of zero entropy automorphisms of X and G0 the set of elements in G which are isotopic to the identity. We prove that, after replacing G by a suitable nite-index subgroup, G/G0 is a unipotent group of derived length at most dimX We also study the algebro-geometric structure of X when it.

2 Introduction: an overview 2. Limited extent of rigidity in traditional dynamics The material presented in this book relies to a considerable extent on the classical theory of (uniform) hyperbolic and partially hyperbolic systems, i.e., the study of rank-one cases of Z+, Z, and R-actions with hyperbolic or partially hyperbolic behavior.

Because each element ofU˜ has zero entropy, T is compact (see ). Let Tˆ be the universal cover of T (thus Tˆ is. 31a (unipotent) abelian real algebraic group, and let exp: Tˆ → T be the covering homomor-phism.

Abstract: Hopf bifurcation in the presence of the symmetric group $S_n$ (acting naturally by permutation of coordinates) is a problem with relevance to coupled oscillatory systems. To study this bifurcation it is important to construct the Taylor expansion of the equivariant vector field in normal form.

We derive generating functions for the numbers of linearly independent invariants. Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem Anatole Katok, Viorel Nitica This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions.

Corollary 2. Let P be a predictive set and (G,Rα) be a compact group rotation by α∈ G. For open sets U⊂ Gand x∈ U, P∩N(x,U) is predictive. Proof. In view of Proposition 1 it is enough to prove that N(x,U) contains a return-time set of a zero entropy ppt. Consider rotation by αon a group G, Uan open set containing the identity e.

Two teams of undergraduates participated in the Mathematical Contest in Modeling. The team of Andrew Harris, Dante Iozzo, and Nigel Michki was designated as "Meritorious Winner" (top 9%) and the team of George Braun, Collin Olander, and Jonathan Tang received honorable mention (top 31%).

John Ringland served as the faculty advisor to both .Group automorphisms as dynamical systems. Thomas Ward (University of East Anglia),This is an overview of some of the problems involved in classifying group automorphisms from the point of view of dynamical systems.

Many of the questions reduce to problems in number theory. Slides from talk.(The latter language has now been abandoned). Gradually, IHES published two annual volumes totalling pages. Sincethe journal has had a circulation of printed copies. It is also available on line and on Les Publications mathématiques de l’IHES is an international journal publishing papers of highest scientific level.