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- D. A. Lind
- 1987

We show that a full solenoid is locally the product of a euclidean component and />-adic components for each rational prime p. An automorphism of a solenoid preserves these components, and its topological entropy is shown to be the sum of the euclidean and p-adic contributions. The p-adic entropy of the corresponding rational matrix is computed using its… (More)

- Manfred Einsiedler, MIKHAIL KAPRANOV, D. A. Lind
- 2004

We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For hypersurfaces this set is also the tropical variety of the defining polynomial. Using non-archimedean analysis and a recent result of Conrad we prove that the amoeba of an… (More)

- D. A. Lind, Klaus Schmidt
- 1996

Let α be an action of Z by continuous automorphisms of a compact abelian group X. A point x in X is called homoclinic for α if αx→ 0X as ‖n‖ → ∞. We study the set ∆α(X) of homoclinic points for α, which is a subgroup of X. If α is expansive then ∆α(X) is at most countable. Our main results are that if α is expansive, then (1) ∆α(x) is nontrivial if and only… (More)

We investigate algebraic Zd-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then… (More)

We give an overview of the field of symbolic dynamics: its history, applications and basic definitions and examples.

Let (Xt,ot) be a shift of finite type, and G = aut(or) denote the group of homeomorphisms of Xt commuting with ctWe investigate the algebraic properties of the countable group G and the dynamics of its action on Xt and associated spaces. Using "marker" constructions, we show G contains many groups, such as the free group on two generators. However, G is… (More)

- D. A. Lind
- SIAM J. Discrete Math.
- 1989

A general framework for investigating topological actions of Zd on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces ofRd . Here we completely describe this expansive behavior for the class of algebraic Zd -actions given by commuting automorphisms of compact abelian groups. The description… (More)

We investigate algebraic Z-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then… (More)

The action of inert automorphisms on finite sets of periodic points of mixing subshifts of finite type is characterized in terms of the sign-gyrationcompatibility condition. The main technique used is variable length coding combined with a “nonnegative algebraic K-theory” formulation of state splitting and merging. One application gives a counterexample to… (More)