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...)|characterization]] of [[cellular automata]] in terms of their [[symbolic dynamics]]. It is named after [[Morton L. Curtis]], [[Gustav A. Hedlund]], and [[Rog ...7 }}.</ref> It has been called "one of the fundamental results in symbolic dynamics".<ref>{{citation ...

...h as a ring of polynomials. Reynolds operators were introduced into fluid dynamics by {{harvs|txt|authorlink=Osbourne Reynolds|first=Osbourne|last= Reynolds|y Reynolds operators are used in fluid dynamics, functional analysis, and invariant theory, and the notation and definition ...

==The invariant set and the symbolic dynamics== Each member of the invariant set can be modelled using [[symbolic dynamics]]: the trajectory is labelled based on each of the discs off of which it re ...

...the [[complex plane]] or other complex [[algebraic varieties]]. Arithmetic dynamics is the study of the number-theoretic properties of [[integer point|integer] ...ic dynamics|p-adic or nonarchimedean dynamics]], is an analogue of complex dynamics in which one replaces the complex numbers {{math|'''C'''}} by a {{mvar|p}}- ...

...her role as Dean, Şahin's research focuses on ergodic theory and symbolic dynamics, areas within dynamical systems that examine the long-term behavior of syst ...

...ces",<ref name=Cornell /> as well as "[[translation surface]]s and complex dynamics in higher dimensions".<ref name=homepage /> ...hematicians]] in Beijing.<ref>{{cite book| chapter=Dynamics in two complex dynamics |first=John |last=Smillie|title=Proceedings of the ICM |location=Beijing |y ...

...ut the methods he used while exploring [[topological entropy]], [[symbolic dynamics]], [[ergodic theory]], [[Markov partition]]s, and [[invariant measure]]s "h * Bowen: "Symbolic Dynamics for Hyperbolic Flows" in '''Proceedings of the International Congress of Ma ...

...eorem:<ref>Gutman, Yonatan. "Embedding ℤk-actions in cubical shifts and ℤk-symbolic extensions." [[Ergodic Theory and Dynamical Systems]] 31.2 (2011): 383-403. ==== [[Symbolic dynamics]] ==== ...

| subjects = [[Foundations of mathematics]], [[Symbolic logic]] ...the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.<ref>Bertrand Russell, ''Principles of Mathematics'' (1903), p ...

| title = Combinatorics, words and symbolic dynamics ...

...lves. A stationary attractor is a state or sets of states where the global dynamics of the network stabilize. Cyclic attractors evolve the network toward a set Various types of attractors may be used to model different types of network dynamics. While fixed-point attractor networks are the most common (originating from ...

The network dynamics described above can be used to support numerous learning operations. We sho ...he knowledge that fusion ART discovers during learning, is compatible with symbolic rule-based representation. Specifically, the recognition categories learned ...

...rrespondence''', which connected structural Ramsey theory to [[topological dynamics]]. ...=September 1978|title=Models Without Indiscernibles|journal=The Journal of Symbolic Logic|volume=43|issue=3|pages=572|doi=10.2307/2273534|issn=0022-4812|jstor= ...

...etry, combinatorics, number theory, you name it. The central assumption of dynamics is that one has a phase space and some group or semigroup of self-maps of t ...College Park|University of Maryland]] where he studied [[Dynamical system|dynamics]]. At Maryland, he lived at "Ergodic House" with Bruce Kitchens, [[Brian Ma ...

...theory|chaotic dynamics]] of spatially extended systems. This includes the dynamics of [[wiktionary:spatiotemporal|spatiotemporal]] [[Chaos theory|chaos]] wher ...=61030071 |isbn=9783540242895}}</ref> Studied systems include [[Population dynamics|populations]], [[chemical reactions]], [[convection]], [[fluid flow]] and [ ...

...Lupacchini, R. (2000) Machines, logic and quantum physics. The Bulletin of Symbolic Logic, 6, 265-283.</ref> In vector logic, this operator can be extended for ...h, I.M. (1948) Matrix development of the calculus of relations. Journal of Symbolic Logic, 13, 193–203</ref> particularly in the use of [[logical matrix|logica ...

| title=Ergodic theory, symbolic dynamics, and hyperbolic spaces (Trieste, 1989) | journal=Conformal Geometry and Dynamics ...

...10.1063/5.0086649 |issn=1054-1500}}</ref> and the study of epidemiological dynamics.<ref>{{cite journal |last1=Schiassi |first1=Enrico |last2=De Florio |first2 ...ramework for Black-Box and Gray-Box identification of chaotic systems with symbolic regression |journal=Chaos, Solitons & Fractals |date=1 November 2024 |volum ...

...f mathematical physics, providing the cornerstone of '''quantum mechanical dynamics in finite-dimensional vector spaces'''.<ref>{{Cite journal | last1 = Santha .../books?id=OpbY_abijtwC&pg=PA101 |title=Clifford Algebras with Numeric and Symbolic Computation Applications |publisher=Birkhäuser |year=1996 |isbn=0-8176-3907 ...

...e Editorial Board of the International Journal of Structural Stability and Dynamics|url=http://www.worldscientific.com/page/ijssd/editorial-board}}</ref><ref>{ ..., Gerhart Schuëller, and I. Elishakoff, (editors), ''Stochastic Structural Dynamics‑Progress in Theory and Applications'', Elsevier Applied Science Publishers, ...