Finite-rank Bratteli–Vershik diagrams are expansive

2008 ◽  
Vol 28 (3) ◽  
pp. 739-747 ◽  
Author(s):  
TOMASZ DOWNAROWICZ ◽  
ALEJANDRO MAASS
Keyword(s):  
Finite Rank ◽  
Main Role ◽  
Fixed Level ◽  
Bounded Number ◽  
Cantor Minimal Systems ◽  
Uniformly Bounded ◽  
The Way

AbstractThe representation of Cantor minimal systems by Bratteli–Vershik diagrams has been extensively used to study particular aspects of their dynamics. A main role has been played by the symbolic factors induced by the way vertices of a fixed level of the diagram are visited by the dynamics. The main result of this paper states that Cantor minimal systems that can be represented by Bratteli–Vershik diagrams with a uniformly bounded number of vertices at each level (called finite-rank systems) are either expansive or topologically conjugate to an odometer. More precisely, when expansive, they are topologically conjugate to one of their symbolic factors.

scholarly journals On the eigenvalues of finite rank Bratteli–Vershik dynamical systems

2009 ◽  
Vol 30 (3) ◽  
pp. 639-664 ◽  
Author(s):  
XAVIER BRESSAUD ◽  
FABIEN DURAND ◽  
ALEJANDRO MAASS
Keyword(s):  
Finite Rank ◽  
Additive Group ◽  
Bratteli Diagram ◽  
Necessary Condition ◽  
Incidence Matrices ◽  
Bounded Number ◽  
Stable Space ◽  
To Come ◽  
Cantor Minimal Systems ◽  
Stable Subspace

AbstractIn this article we study conditions to be a continuous or a measurable eigenvalue of finite rank minimal Cantor systems, that is, systems given by an ordered Bratteli diagram with a bounded number of vertices per level. We prove that continuous eigenvalues always come from the stable subspace associated with the incidence matrices of the Bratteli diagram and we study rationally independent generators of the additive group of continuous eigenvalues. Given an ergodic probability measure, we provide a general necessary condition for there to be a measurable eigenvalue. Then, we consider two families of examples, a first one to illustrate that measurable eigenvalues do not need to come from the stable space. Finally, we study Toeplitz-type Cantor minimal systems of finite rank. We recover classical results in the continuous case and we prove that measurable eigenvalues are always rational but not necessarily continuous.

scholarly journals On topological rank of factors of Cantor minimal systems

2021 ◽  
pp. 1-24
Author(s):  
NASSER GOLESTANI ◽  
MARYAM HOSSEINI
Keyword(s):  
Dynamical System ◽  
Finite Rank ◽  
Affirmative Answer ◽  
Cantor Set ◽  
Minimal System ◽  
Full Generality ◽  
Cantor Minimal Systems ◽  
Minimal Dynamical System ◽  
Uniformly Bounded

Abstract A Cantor minimal system is of finite topological rank if it has a Bratteli–Vershik representation whose number of vertices per level is uniformly bounded. We prove that if the topological rank of a minimal dynamical system on a Cantor set is finite, then all its minimal Cantor factors have finite topological rank as well. This gives an affirmative answer to a question posed by Donoso, Durand, Maass, and Petite in full generality. As a consequence, we obtain the dichotomy of Downarowicz and Maass for Cantor factors of finite-rank Cantor minimal systems: they are either odometers or subshifts.

Colonial Modernity and Methodological Nationalism: The Structuring of Sociological Traditions of India

2017 ◽  
Vol 66 (2) ◽  
pp. 125-144 ◽  
Author(s):  
Sujata Patel
Keyword(s):  
Academic Discipline ◽  
Main Role ◽  
Characteristic Mode ◽  
Teaching And Research ◽  
Professional Orientation ◽  
Colonial Modernity ◽  
Methodological Nationalism ◽  
History Of ◽  
Four Levels ◽  
The Way

This article traces traditions of sociological thinking in India and suggests that in order to write the disciplines’ history, it is important to identify the episteme that governs these traditions. It suggests that there are two broad epistemes that have defined sociology as a discipline in India—colonial modernity and methodological nationalism—and it argues that they organise theories, perspectives, methodologies and methods, teaching and research practices of the discipline. The history of the imprint of these epistemes is investigated at four levels: first, in the way one or both defined the discipline’s identity and, thus, organised its characteristic mode of thinking methodologically; second, in the way this identity defined its theoretical direction and the theories that it borrowed, adapted to and reframed; third, in the way the first two organised its professional orientation and made it choose its identity as an academic discipline whose main role is restricted to teaching and research within academic institutions at an expense of a public orientation; and fourth, the way the aforementioned three defined its geographical compass, limiting its queries to national concerns wherein the macro became reduced to the micro abjuring discussions on global debates. This article suggests that today there is a crisis in the received epistemes, and in this context, it becomes imperative to take command to define a new episteme which intersects the local, regional, national and global concerns, is theoretical and methodologically eclectic and is comparative in nature.

scholarly journals Memory, Place and Pain in W.G. Sebald's: The Emigrants

2021 ◽  
Vol 8 (2) ◽  
pp. 154-172
Author(s):  
Kobi (Yaaqov) Assoulin
Keyword(s):  
Main Role ◽  
The Novel ◽  
Human Beings ◽  
Do So ◽  
The Way ◽  
At Home

When we discuss the concept of place, we mostly do so geographically, or as a metaphor. That is, by representing what we think about by geographical notions. This paper avoids this literary tendency by discussing directly the role of actual place in W.G. Sebald's The Emigrants. Not only that, While still acknowledging melancholy's main role in the novel, and the way in which it is discussed in Freud and through Freud et al, the paper takes this melancholy to be a phenomenological spring board for explicating the centrality of place within The Emigrants's melancholy. In order to do this, the paper discusses the role of place within major phenomenological thinkers like Husserl, Heidegger and Merleau-Ponty and the way their discussion dissolves the classical dichotomy of subject/object. However, as this dichotomy is dissolved, it becomes clearer as to the way places do not only belong to human-beings – simultaneously, humans belong to places. Through explicating this, we come to understand in The Emigrants what makes it such a tragic story. While the emigrants find their home to be rooted in places and memories of places, these places carry at the same time a mood of being-at-home and alongside that, a sense of ruins which haunt. Thus they become trapped between the conflicting urges of running toward and running from these memories. A dilemma that is finally solved only, in the novel, through death.

scholarly journals administrasi kepemimpinan pendidikan

2020 ◽  
Author(s):  
Elsa puji kurnia
Keyword(s):  
Decision Making ◽  
Educational Leadership ◽  
Leadership Style ◽  
Educational Goals ◽  
Main Role ◽  
Or Organization ◽  
The Way

Leadership is the way the leader influences the behavior of his subordinates , in order to cooperate and work productively for the sake of achievement of goals from the organization. The leadership style of a leader in motivating employees to carry out company activities will determine the performance of the company or organization. In relationship leaders with subordinates, a number of employees of expect to get treatment of leaders who are open and provide flexibility in work, while others hope that the leadership corrects results more bad work because this will make subordinates work less productive and less partisipating in decision making. Leadersip is park of management, namely planning and organizing, but the main role of leadership is to influence other people to achieve their stated goals. Educational leadership is theability to drive the implementation of education, so that educational goals that have been set can be achieved affectively and afficiently .

scholarly journals Posłuszeństwo monastyczne w prawodawstwie pachomiańskim i bazyliańskim

Vox Patrum ◽  
2016 ◽  
Vol 65 ◽  
pp. 129-140
Author(s):  
Marianna Ciemała
Keyword(s):  
Main Role ◽  
Community Life ◽  
Word Of God ◽  
Rule Of Life ◽  
Close Relationship ◽  
Sacred Scripture ◽  
The Way

Obedience was one of the fundamental principles of community life in monas­teries in the first centuries. Based on the analysis of the texts of St. Pachomius’ and St. Basil’s legislation, the article addresses the issue of different correlations taking place within the framework of monastic obedience. The texts of the Rule of St. Pachomius as well as of the Asketikon of St. Basil the Great show that in the ceno­bitical life there was a close relationship between obedience to God, to His word, to the rule of life, to superiors, and, to some extent even to all brothers. Sacred Scripture was considered the primary, or even the only, rule of life for the ceno­bites. Both the Pachomius and Basil in their Rules put a strong accent on obedience to God, which, in practice, was realized in keeping His commandments. The main role of superiors was to lead the brothers to the fullness of salvation. They were to do it with care and responsibility. The analysis of the texts on superiors found that they indicated that the superiors had the obligation to be the first in keeping the God’s commandments as well as in obeying the Rule and the precepts of the elders. Obedience to superiors was understood as being the same as obedience to God, but was dependent according to the way the superiors fulfill their dutes of preaching the word of God and living their lives in agreement to their teaching.

scholarly journals administrasi kepemimpinan pendidikan

2020 ◽  
Author(s):  
Nurhayati
Keyword(s):  
Decision Making ◽  
Educational Leadership ◽  
Leadership Style ◽  
Educational Goals ◽  
Main Role ◽  
Or Organization ◽  
The Way

Leadership is the way the leader influences the behavior of his subordinates , in order to cooperate and work productively for the sake of achievement of goals from the organization. The leadership style of a leader in motivating employees to carry out company activities will determine the performance of the company or organization. In relationship leaders with subordinates, a number of employees of expect to get treatment of leaders who are open and provide flexibility in work, while others hope that the leadership corrects results more bad work because this will make subordinates work less productive and less partisipating in decision making. Leadersip is park of management, namely planning and organizing, but the main role of leadership is to influence other people to achieve their stated goals. Educational leadership is theability to drive the implementation of education, so that educational goals that have been set can be achieved affectively and afficiently

scholarly journals Pentingnya kepemimpinan dalam dunia pendidikan

2019 ◽  
Author(s):  
Rachmat Alrivan
Keyword(s):  
Decision Making ◽  
Educational Leadership ◽  
Leadership Style ◽  
Educational Goals ◽  
Main Role ◽  
Or Organization ◽  
Ability To Drive ◽  
The Way

Leadership is the way the leader influences thebehavior of his subordinates , in order to cooperate and workproductively for the sake of achievement of goals from theorganization. The leadership style of a leader in motivatingemployees to carry out company activities will determine theperformance of the company or organization. In relationshipleaders with subordinates, a number of employees of expect to gettreatment of leaders who are open and provide flexibility inwork, while others hope that the leadership corrects results morebad work because this will make subordinates work less productive and less partisipating in decision making. Leadersip ispark of management, namely planning and organizing, but the main role of leadership is to influence other people to achievetheir stated goals. Educational leadership is the ability to drive the implementation of education, so that educational goals that have been set can be achieved affectively and afficiently.

scholarly journals Pentingnya pemberian layanan khusus kepada peserta didik

2019 ◽  
Author(s):  
Rachmat Alrivan
Keyword(s):  
Decision Making ◽  
Educational Leadership ◽  
Leadership Style ◽  
Educational Goals ◽  
Main Role ◽  
Or Organization ◽  
Ability To Drive ◽  
The Way

Leadership is the way the leader influences thebehavior of his subordinates , in order to cooperate and workproductively for the sake of achievement of goals from theorganization. The leadership style of a leader in motivatingemployees to carry out company activities will determine theperformance of the company or organization. In relationshipleaders with subordinates, a number of employees of expect to gettreatment of leaders who are open and provide flexibility inwork, while others hope that the leadership corrects results morebad work because this will make subordinates work less productive and less partisipating in decision making. Leadersip ispark of management, namely planning and organizing, but the main role of leadership is to influence other people to achievetheir stated goals. Educational leadership is the ability to drive the implementation of education, so that educational goals that have been set can be achieved affectively and afficiently

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