Displaying similar documents to “On U-equivalence spaces”

Equivalence of ill-posed dynamical systems

Tomoharu Suda (2023)

Archivum Mathematicum

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The problem of topological classification is fundamental in the study of dynamical systems. However, when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence. For example, when a system has trajectories distinguished only by parametrization, we cannot apply the usual definition of equivalence based on the phase space, which presupposes the uniqueness of trajectories. In this study, we formulate a notion of “topological equivalence” using...

Relational quotients

Miodrag Sokić (2013)

Fundamenta Mathematicae

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Let 𝒦 be a class of finite relational structures. We define ℰ𝒦 to be the class of finite relational structures A such that A/E ∈ 𝒦, where E is an equivalence relation defined on the structure A. Adding arbitrary linear orderings to structures from ℰ𝒦, we get the class 𝒪ℰ𝒦. If we add linear orderings to structures from ℰ𝒦 such that each E-equivalence class is an interval then we get the class 𝒞ℰ[𝒦*]. We provide a list of Fraïssé classes among ℰ𝒦, 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*]. In addition,...

On conjugacy equation in dimension one

Krzysztof Ciepliński, Zbigniew Leśniak (2013)

Banach Center Publications

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In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.

A natural occurrence of shift equivalence

Fatma Muazzez Şımşır, Cem Tezer (2011)

Annales Polonici Mathematici

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A natural occcurrence of shift equivalence in a purely algebraic setting is exhibited.