Canonical symbolic dynamics for one-dimensional generalized solenoids

Abstract

Abstract. We define canonical subshift of finite type covers for Williams' onedimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

Homology for one-dimensional solenoids

“…The main goal of this paper is to compute the homology of onedimensional generalized solenoids, defined by K. Thomsen, based on an earlier work of Yi [11,17]. The solenoids were defined first by Williams on manifolds, and then generalized by Yi on topological spaces [14,15,17], but also see [16]. We first quickly review the Thomsen's definition [11].…”

“…Following Williams and Yi [15,17], Thomsen called (X, f ) a generalized one-dimensional solenoid or just a one-solenoid [11]. Definition 2.2.…”

“…The main goal of this paper is to compute the homology of onedimensional generalized solenoids defined by Williams [14,15], generalized by Inhyeop Yi [17] and later by Klaus Thomsen [11]. In fact these spaces are inverse limits of finite graphs with one expanding map f .…”

Markov partitions and homology for -solenoids

“…We also mention that this homology has been computed on rather different solenoids of a more topological nature first constructed by Williams [13] and later studied by Yi [15] and Thomsen [10] as inverse limits of branched 1-manifolds by the second author with Amini and Gholikandi [1].…”

Обратимые Расширения Необратимых Динамических Систем: $C^*$-Метод

“…замечание 3.10), множество M ∞ по сути совпа-дает с пространством обратного предела соответствующей последовательности отображений. Описанию пространств подобного типа посвящены многочислен-ные исследования; большое количество результатов на эту тему можно найти, например, в [9]- [18], помимо этого на базе развитой в настоящей работе техники в [19] получено описание обратимых расширений унимодальных отображений отрезка.…”