Jℱ-Class Weighted Backward Shifts

In this article [Formula: see text]-class operators are introduced and some basic properties of [Formula: see text]-vectors are given. The [Formula: see text]-class operators include the [Formula: see text]-class operators and [Formula: see text]-class operators introduced by Costakis and Manoussos in 2008. This class also includes the [Formula: see text]-class and [Formula: see text]-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fréchet sequence space, we establish a criterion under which the shift operators belong to the [Formula: see text]-class. From the criterion it is easy to obtain the existing criteria of hypercyclic backward shifts and of the topological mixing backward shifts. The obtained criterion also reveals the characteristic of [Formula: see text]-class shift operators by the recurrence property. Meanwhile, we obtain infinite topological entropy when the shifts have stronger recurrence property, which generalizes the related results by Brian et al. in 2017.

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Topological mixing, knot points and bounds of topological entropy

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2015.20.3547 ◽

2015 ◽

Vol 20 (10) ◽

pp. 3547-3564

Author(s):

Piotr Oprocha ◽

◽

Paweł Potorski ◽

Keyword(s):

Topological Entropy ◽

Topological Mixing

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PREIMAGE ENTROPY FOR MAPPINGS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499001309 ◽

1999 ◽

Vol 09 (09) ◽

pp. 1815-1843 ◽

Cited By ~ 22

Author(s):

ZBIGNIEW NITECKI ◽

FELIKS PRZYTYCKI

Keyword(s):

Topological Entropy ◽

Basic Properties ◽

The Past ◽

Noninvertible Maps ◽

Analogous Behavior

Several entropy-like invariants have been defined for noninvertible maps, based on various ways of measuring the dispersion of preimages and preimage sets in the past. We investigate basic properties of four such invariants, finding that their behavior in some ways differs sharply from the analogous behavior for topological entropy.

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On triple sequence space of Bernstein Stancu Cheney and Sharma operator of rough I_lambda-convergence of weight g

Mathematica ◽

10.24193/mathcluj.2021.1.09 ◽

2021 ◽

Vol 63 (86) (1) ◽

pp. 98-110

Author(s):

Arulmani Indumathi ◽

Ayhan Esi ◽

Nagarajan Subramanian

Keyword(s):

Sequence Space ◽

Basic Properties

We introduce and study some basic properties of rough I_lambda-convergence of weight g, where g is a function statisying certain conditions, of a triple sequence of Bernstein Stancu Cheney and Sharma operators and also investigate certain properties of rough I_lambda-convergence of weight g.

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Fully positive topological entropy and topological mixing

Symbolic Dynamics and its Applications - Contemporary Mathematics ◽

10.1090/conm/135/1185082 ◽

1992 ◽

pp. 95-105 ◽

Cited By ~ 29

Author(s):

F. Blanchard

Keyword(s):

Topological Entropy ◽

Topological Mixing ◽

Positive Topological Entropy

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CHAOS FOR BACKWARD SHIFT OPERATORS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402005418 ◽

2002 ◽

Vol 12 (08) ◽

pp. 1703-1715 ◽

Cited By ~ 30

Author(s):

F. MARTÍNEZ-GIMÉNEZ ◽

A. PERIS

Keyword(s):

Dynamical Systems ◽

Differential Operator ◽

Applied Mathematics ◽

Linear Dynamical Systems ◽

Infinite Dimensional ◽

Shift Operators ◽

Rich Variety ◽

Backward Shift ◽

Backward Shifts ◽

Spaces Of Analytic Functions

Backward shift operators provide a general class of linear dynamical systems on infinite dimensional spaces. Despite linearity, chaos is a phenomenon that occurs within this context. In this paper we give characterizations for chaos in the sense of Auslander and Yorke [1980] and in the sense of Devaney [1989] of weighted backward shift operators and perturbations of the identity by backward shifts on a wide class of sequence spaces. We cover and unify a rich variety of known examples in different branches of applied mathematics. Moreover, we give new examples of chaotic backward shift operators. In particular we prove that the differential operator I + D is Auslander–Yorke chaotic on the most usual spaces of analytic functions.

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SOME NONROBUST BERNOULLI-SHIFT RULES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024840 ◽

2009 ◽

Vol 19 (10) ◽

pp. 3407-3415 ◽

Cited By ~ 4

Author(s):

LIN CHEN ◽

FANGYUE CHEN ◽

WEIFENG JIN ◽

FANGFANG CHEN ◽

GUANRONG CHEN

Keyword(s):

Cellular Automata ◽

Topological Entropy ◽

Sequence Space ◽

Bernoulli Shift ◽

Binary Sequence ◽

Class I ◽

Positive Topological Entropy ◽

Elementary Cellular Automata ◽

Topologically Mixing ◽

Shift Dynamics

In this paper, it is shown that elementary cellular automata rule 172, as a member of the Chua's robust period-1 rules and the Wolfram class I, is also a nonrobust Bernoulli-shift rule. This rule actually exhibits complex Bernoulli-shift dynamics in the bi-infinite binary sequence space. More precisely, in this paper, it is rigorously proved that rule 172 is topologically mixing and has positive topological entropy on a subsystem. Hence, rule 172 is chaotic in the sense of both Li–Yorke and Devaney. The method developed in this paper is also applicable to checking the subshifts contained in other robust period-1 rules, for example, rules 168 and 40, which also represent nonrobust Bernoulli-shift dynamics.

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Minimality, transitivity, mixing and topological entropy on spaces with a free interval

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385712000442 ◽

2012 ◽

Vol 33 (6) ◽

pp. 1786-1812 ◽

Cited By ~ 11

Author(s):

MATÚŠ DIRBÁK ◽

ĽUBOMÍR SNOHA ◽

VLADIMÍR ŠPITALSKÝ

Keyword(s):

Topological Entropy ◽

Open Subset ◽

Topological Structure ◽

Open Interval ◽

Topological Transitivity ◽

Topological Mixing ◽

Minimal Sets ◽

Free Interval ◽

Continuous Maps ◽

Metrizable Spaces

AbstractWe study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e. an open subset homeomorphic to an open interval). Special attention is paid to relationships between topological transitivity, weak and strong topological mixing, dense periodicity and topological entropy as well as to the topological structure of minimal sets. In particular, a trichotomy for minimal sets and a dichotomy for transitive maps are proved.

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The visuospatial imagery of sequence-space synaesthesia

PsycEXTRA Dataset ◽

10.1037/e512592013-262 ◽

2011 ◽

Author(s):

M. Price

Keyword(s):

Sequence Space

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On the Essence and Tipology of International Public Goods

Voprosy Ekonomiki ◽

10.32609/0042-8736-2005-3-131-141 ◽

2005 ◽

pp. 131-141

Author(s):

V. Mortikov

Keyword(s):

Economic Policy ◽

Social Construction ◽

Public Goods ◽

Public Good ◽

Global Public Goods ◽

Club Goods ◽

Basic Properties ◽

International Public Goods ◽

Regional Public Goods ◽

Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

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