scholarly journals Projective subdynamics and universal shifts

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Pierre Guillon
Keyword(s):  
Large Class ◽  
Finite Type ◽  
Positive Entropy ◽  
Two Dimensional ◽  
One Dimensional ◽  
International Audience

International audience We study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics.

scholarly journals Topologically completely positive entropy and zero-dimensional topologically completely positive entropy

2017 ◽  
Vol 38 (5) ◽  
pp. 1894-1922
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Positive Entropy ◽  
Two Dimensional ◽  
Completely Positive ◽  
Shift Of Finite Type ◽  
One Dimensional ◽  
Zero Entropy ◽  
The Difference

In a previous paper [Pavlov, A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065], the author gave a characterization for when a $\mathbb{Z}^{d}$-shift of finite type has no non-trivial subshift factors with zero entropy, a property which we here call zero-dimensional topologically completely positive entropy. In this work, we study the difference between this notion and the more classical topologically completely positive entropy of Blanchard. We show that there are one-dimensional subshifts and two-dimensional shifts of finite type which have zero-dimensional topologically completely positive entropy but not topologically completely positive entropy. In addition, we show that strengthening the hypotheses of the main result of Pavlov [A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065] yields a sufficient condition for a $\mathbb{Z}^{d}$-shift of finite type to have topologically completely positive entropy.

scholarly journals One-dimensional and two-dimensional dynamics of cubic maps

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Djellit Ilhem ◽  
Kara Amel
Keyword(s):  
Large Class ◽  
System Parameter ◽  
Two Dimensional ◽  
One Dimensional ◽  
Henon Maps ◽  
Hénon Maps ◽  
Starting Point ◽  
Good Starting Point ◽  
Polynomial Diffeomorphisms

We concentrate on the dynamics of one-dimensional and two-dimensional cubic maps, it describes how complex behaviors can possibly arise as a system parameter changes. This is a large class of diffeomorphisms which provide a good starting point for understanding polynomial diffeomorphisms with constant Jacobian and equivalent to a composition of generalized Hénon maps. Due to the theoretical and practical difficulties involved in the study, computers will presumably play a role in such efforts.

scholarly journals A stronger recognizability condition for two-dimensional languages

2013 ◽  
Vol Vol. 15 no. 2 (Automata, Logic and Semantics) ◽  
Author(s):  
Marcella Anselmo ◽  
Maria Madonia
Keyword(s):  
Finite Automata ◽  
The Other ◽  
Two Dimensional ◽  
Minimal Size ◽  
One Dimensional ◽  
Tiling System ◽  
International Audience ◽  
The One

Automata, Logic and Semantics International audience The paper presents a condition necessarily satisfied by (tiling system) recognizable two-dimensional languages. The new recognizability condition is compared with all the other ones known in the literature (namely three conditions), once they are put in a uniform setting: they are stated as bounds on the growth of some complexity functions defined for two-dimensional languages. The gaps between such functions are analyzed and examples are shown that asymptotically separate them. Finally the new recognizability condition results to be the strongest one, while the remaining ones are its particular cases. The problem of deciding whether a two-dimensional language is recognizable is here related to the one of estimating the minimal size of finite automata recognizing a sequence of (one-dimensional) string languages.

GENERALLY t-LINKATIVE DOMAINS

2012 ◽  
Vol 11 (02) ◽  
pp. 1250027
Author(s):  
THOMAS G. LUCAS
Keyword(s):  
Finite Type ◽  
Maximal Ideal ◽  
Integral Domain ◽  
Type System ◽  
Nonzero Ideal ◽  
Two Dimensional ◽  
Finitely Generated ◽  
One Dimensional ◽  
Valuation Domains ◽  
Prüfer Domains

An overring t of an integral domain R is t-linked over R if for each finitely generated nonzero ideal I of R, (T : IT) ⊋ T implies (R : I) ⊋ R. A t-linkative domain is one for which each overring is t-linked. The notion of a generally t-linkative domain is introduced as a domain R such that [Formula: see text] is t-linkative for each finite type system of ideals [Formula: see text]. In general, R is generally t-linkative if and only if RM is generally t-linkative for each maximal ideal M. All Prüfer domains are generally t-linkative as are all one-dimensional domains and all pseudo-valuation domains. If R is Noetherian and not a field, then it is generally t-linkative if and only if it is one-dimensional. In contrast, an example is given of a two-dimensional Mori domain that is generally t-linkative.

scholarly journals Embedding Bratteli–Vershik systems in cellular automata

2009 ◽  
Vol 30 (5) ◽  
pp. 1561-1572 ◽  
Author(s):  
MARCUS PIVATO ◽  
REEM YASSAWI
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Finite Type ◽  
Two Dimensional ◽  
Time Diagram ◽  
Constant Length ◽  
Subshift Of Finite Type ◽  
One Dimensional ◽  
Toeplitz Systems

AbstractMany dynamical systems can be naturally represented as Bratteli–Vershik (or adic) systems, which provide an appealing combinatorial description of their dynamics. If an adic system X is linearly recurrent, then we show how to represent X using a two-dimensional subshift of finite type Y; each ‘row’ in a Y-admissible configuration corresponds to an infinite path in the Bratteli diagram of X, and the vertical shift on Y corresponds to the ‘successor’ map of X. Any Y-admissible configuration can then be recoded as the space-time diagram of a one-dimensional cellular automaton Φ; in this way X is embedded in Φ (i.e. X is conjugate to a subsystem of Φ). With this technique, we can embed many odometers, Toeplitz systems, and constant-length substitution systems in one-dimensional cellular automata.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

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