Journal of Symbolic Logic, ISSN 0022-4812, 06/2018, Volume 83, Issue 2, pp. 477 - 495

AbstractThe shift map σ on ω* is the continuous self-map of ω* induced by the function n ↦ n + 1 on ω. Given a compact Hausdorff space X and a continuous...

weak incompressibility | Parovičenko's theorem | Martin's Axiom | shift map | elementary submodels | Continuum Hypothesis | abstract omega-limit sets | Stone-Čech compactification

weak incompressibility | Parovičenko's theorem | Martin's Axiom | shift map | elementary submodels | Continuum Hypothesis | abstract omega-limit sets | Stone-Čech compactification

Journal Article

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 08/2016, Volume 26, Issue 9, p. 1650150

Let X be a local dendrite and let f : X → X be a monotone map. Denote by P ( f ) , RR ( f ) , UR ( f ) , R ( f ) the set of periodic (resp., regularly...

hyperspace | dendrite | monotone map | ω -limit set | recurrent | graph | Hausdorff metric | local dendrite | OMEGA-LIMIT SETS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | omega-limit set

hyperspace | dendrite | monotone map | ω -limit set | recurrent | graph | Hausdorff metric | local dendrite | OMEGA-LIMIT SETS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | omega-limit set

Journal Article

Journal of Topology and Analysis, ISSN 1793-5253, 2019

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2017, Volume 369, Issue 1, pp. 139 - 165

An arcwise connected compact metric space X is called a quasi-graph if there is a positive integer N with the following property: for every arcwise connected...

INTERVAL | MATHEMATICS | periodic point | omega-limit point | (P)OVER-BAR | POINTS | recurrent point | (R)OVER-BAR | DEPTH | graph | Quasi-graph

INTERVAL | MATHEMATICS | periodic point | omega-limit point | (P)OVER-BAR | POINTS | recurrent point | (R)OVER-BAR | DEPTH | graph | Quasi-graph

Journal Article

Topology and its Applications, ISSN 0166-8641, 04/2019, Volume 257, pp. 1 - 10

In this note we present some results on typical properties of the chain recurrent sets of bounded Baire one functions. In particular we show that typical...

Residual set | Chain recurrent set | Typical functions | k-continuous functions | Interval maps | Baire one functions | OMEGA-LIMIT SETS | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMICS

Residual set | Chain recurrent set | Typical functions | k-continuous functions | Interval maps | Baire one functions | OMEGA-LIMIT SETS | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMICS

Journal Article

Nonlinearity, ISSN 0951-7715, 01/2019, Volume 32, Issue 1, pp. 285 - 300

We prove that the Mobius disjointness conjecture holds for graph maps with zero topological entropy and for all monotone local dendrite maps. We further show...

minimal set | Möbius disjointness conjecture | Sarnak conjecture | dendrite | ω-limit set | graph, local dendrite | Möbius function | IMPLIES | MATHEMATICS, APPLIED | INTERVAL MAPS | GRAPH MAPS | ZERO ENTROPY | PHYSICS, MATHEMATICAL | graph | local dendrite | Mobius disjointness conjecture | CHAOS | CHOWLA | OMEGA-LIMIT-SETS | DYNAMICS | SYSTEMS | Mobius function | TOPOLOGICAL-ENTROPY | omega-limit set | Mathematics - Dynamical Systems

minimal set | Möbius disjointness conjecture | Sarnak conjecture | dendrite | ω-limit set | graph, local dendrite | Möbius function | IMPLIES | MATHEMATICS, APPLIED | INTERVAL MAPS | GRAPH MAPS | ZERO ENTROPY | PHYSICS, MATHEMATICAL | graph | local dendrite | Mobius disjointness conjecture | CHAOS | CHOWLA | OMEGA-LIMIT-SETS | DYNAMICS | SYSTEMS | Mobius function | TOPOLOGICAL-ENTROPY | omega-limit set | Mathematics - Dynamical Systems

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 07/2018, Volume 265, Issue 2, pp. 702 - 718

It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak...

Weak attractor | Omega limit set | Compact random set | Forward attractor | Closed random set | Pullback attractor | MATHEMATICS | RANDOM DYNAMICAL-SYSTEMS

Weak attractor | Omega limit set | Compact random set | Forward attractor | Closed random set | Pullback attractor | MATHEMATICS | RANDOM DYNAMICAL-SYSTEMS

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2017, Volume 23, Issue 9, pp. 1485 - 1490

In this paper, we study some qualitative properties of homeomorphisms of regular curves. We prove among other things that if f is a homeomorphism of a regular...

minimal set | Regular curve | 37B45 | periodic point | 37E99 | 37B05 | limit set | homeomorphisms | MATHEMATICS, APPLIED | MAPS | CONTINUA | SETS | alpha-limit set | TOPOLOGICAL-ENTROPY | omega-limit set | Applied mathematics

minimal set | Regular curve | 37B45 | periodic point | 37E99 | 37B05 | limit set | homeomorphisms | MATHEMATICS, APPLIED | MAPS | CONTINUA | SETS | alpha-limit set | TOPOLOGICAL-ENTROPY | omega-limit set | Applied mathematics

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 01/2018, Volume 106, pp. 5 - 15

Based on the famous Shimizu–Morioka system, this paper proposes a novel five-dimensional Shimizu–Morioka-type hyperchaotic system that has an infinite set of...

5D Hyperchaotic system | Ellipse-parabola-type and hyperbola-parabola-type heteroclinic orbits | Singularly degenerate heteroclinic cycle | ω–Limit set and α–limit set | Lyapunov function | EXISTENCE | CHAOTIC SYSTEM | TRICOMI PROBLEM | PHYSICS, MULTIDISCIPLINARY | omega-Limit set and alpha-limit set | BIFURCATIONS | HOMOCLINIC TRAJECTORIES | PHYSICS, MATHEMATICAL | SHIMIZU-MORIOKA | ATTRACTORS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LORENZ-TYPE SYSTEM | DYNAMICS | EQUATION

5D Hyperchaotic system | Ellipse-parabola-type and hyperbola-parabola-type heteroclinic orbits | Singularly degenerate heteroclinic cycle | ω–Limit set and α–limit set | Lyapunov function | EXISTENCE | CHAOTIC SYSTEM | TRICOMI PROBLEM | PHYSICS, MULTIDISCIPLINARY | omega-Limit set and alpha-limit set | BIFURCATIONS | HOMOCLINIC TRAJECTORIES | PHYSICS, MATHEMATICAL | SHIMIZU-MORIOKA | ATTRACTORS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LORENZ-TYPE SYSTEM | DYNAMICS | EQUATION

Journal Article

Topology and its Applications, ISSN 0166-8641, 08/2016, Volume 209, pp. 33 - 45

This paper investigates the structure of points u∈AN that are such that the omega-limit set ω(u,σ) is precisely X, where X⊆AN is an internally transitive shift...

Minimal Cantor sets | Unimodal maps | Shift spaces | Omega-limit sets | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCES

Minimal Cantor sets | Unimodal maps | Shift spaces | Omega-limit sets | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCES

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2014, Volume 2014, Issue 1, pp. 1 - 9

In this paper we mainly study the weakly mixing sets and transitive sets of non-autonomous discrete systems. Some basic concepts are introduced for...

Ordinary Differential Equations | weakly mixing set | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | transitive set | Mathematics | non-autonomous discrete system | Partial Differential Equations | OMEGA-LIMIT SETS | MATHEMATICS | CHAOS | MATHEMATICS, APPLIED | DYNAMICAL-SYSTEMS | ENTROPY | Differential equations | Difference equations | Discrete systems

Ordinary Differential Equations | weakly mixing set | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | transitive set | Mathematics | non-autonomous discrete system | Partial Differential Equations | OMEGA-LIMIT SETS | MATHEMATICS | CHAOS | MATHEMATICS, APPLIED | DYNAMICAL-SYSTEMS | ENTROPY | Differential equations | Difference equations | Discrete systems

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2013, Volume 33, Issue 5, pp. 1819 - 1833

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2017, Volume 55, Issue 6, pp. 4048 - 4071

In this paper, we investigate synchronization issues in heterogeneous complex networks. We start with a necessary condition for the existence of synchronous...

Heterogeneous networks | Lyapunov functions | Invariant set | ω-limit set | Synchronization | TARGET | heterogeneous networks | MATHEMATICS, APPLIED | STABILITY | invariant set | MULTIAGENT SYSTEMS | CONSENSUS | ADAPTIVE-CONTROL | COMPLEX DYNAMICAL NETWORKS | synchronization | BOUNDED SYNCHRONIZATION | COUPLED OSCILLATORS | MULTIPLE LYAPUNOV FUNCTIONS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | omega-limit set

Heterogeneous networks | Lyapunov functions | Invariant set | ω-limit set | Synchronization | TARGET | heterogeneous networks | MATHEMATICS, APPLIED | STABILITY | invariant set | MULTIAGENT SYSTEMS | CONSENSUS | ADAPTIVE-CONTROL | COMPLEX DYNAMICAL NETWORKS | synchronization | BOUNDED SYNCHRONIZATION | COUPLED OSCILLATORS | MULTIPLE LYAPUNOV FUNCTIONS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | omega-limit set

Journal Article

数学学报：英文版, ISSN 1439-8516, 2018, Volume 34, Issue 2, pp. 194 - 208

Let G be a graph and f： G → G be a continuous map. Denote by h（f）, P（f）, AP（f）, R（f） and w（x, f） the topological entropy of f, the set of periodic points of f,...

37B40 | 54H20 | Topological entropy | periodic point | Mathematics, general | Mathematics | ω -limit set | 37E25 | recurrent point | ω-limit set | MATHEMATICS | MATHEMATICS, APPLIED | POINTS | omega-limit set | Mapping | Entropy | Graph theory | Topology | Mathematical analysis

37B40 | 54H20 | Topological entropy | periodic point | Mathematics, general | Mathematics | ω -limit set | 37E25 | recurrent point | ω-limit set | MATHEMATICS | MATHEMATICS, APPLIED | POINTS | omega-limit set | Mapping | Entropy | Graph theory | Topology | Mathematical analysis

Journal Article

Topology and its Applications, ISSN 0166-8641, 09/2019, Volume 265, p. 106821

Let I=[0,1], with bB2 the set of bounded Baire-2 self-maps of I. The set bB2 is closely related to the collection of measurable functions, as g:I→I is...

Baire-2 function | Trajectory | ω-Limit set | Generic | omega-Limit set | MATHEMATICS | MATHEMATICS, APPLIED | MAPS

Baire-2 function | Trajectory | ω-Limit set | Generic | omega-Limit set | MATHEMATICS | MATHEMATICS, APPLIED | MAPS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 2, pp. 649 - 654

A continuous map f from a graph G to itself is called a graph map. Denote by P ( f ) , R ( f ) , ω ( f ) , Ω ( f ) and CR ( f ) the sets of periodic points,...

Periodic point | Recurrent point | ω-limit point | Graph map | INTERVAL | MATHEMATICS | MATHEMATICS, APPLIED | omega-limit point | CHAIN RECURRENT SET

Periodic point | Recurrent point | ω-limit point | Graph map | INTERVAL | MATHEMATICS | MATHEMATICS, APPLIED | omega-limit point | CHAIN RECURRENT SET

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 06/2016, Volume 87, pp. 17 - 18

Let X be a dendrite. We say that X has the APR-property provided that for each continuous self-mapping f of X, AP(f)¯=R(f)¯, where AP(f) and R(f) are the sets...

Dendrite map | Minimal set | Recurrent | ω-limit set | Periodic | Almost periodic point | Dendrite | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | DENDROIDS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MAPS | END-POINTS | omega-limit set

Dendrite map | Minimal set | Recurrent | ω-limit set | Periodic | Almost periodic point | Dendrite | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | DENDROIDS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MAPS | END-POINTS | omega-limit set

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2014, Volume 266, Issue 6, pp. 3455 - 3507

This paper studies the Cauchy problem for a parabolic–elliptic system in R2 modeling chemotaxis as well as self-attracting particles. In the critical mass case...

Oscillating solutions | Omega limit sets | Chemotaxis system | Steady-states

Oscillating solutions | Omega limit sets | Chemotaxis system | Steady-states

Journal Article

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, ISSN 1023-6198, 2011, Volume 17, Issue 12, pp. 1793 - 1799

Let f and g be elements of C(I, I) with x is an element of I. We studyv-limit sets omega(x,[f, g]) generated by alternating trajectories of the form tau(x, [f,...

INTERVAL | MATHEMATICS, APPLIED | topological semiconjugation | continuous alternating system | DIFFERENCE-EQUATIONS | omega-limit set | Intervals | Trajectories | Difference equations | Unions

INTERVAL | MATHEMATICS, APPLIED | topological semiconjugation | continuous alternating system | DIFFERENCE-EQUATIONS | omega-limit set | Intervals | Trajectories | Difference equations | Unions

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 2014, Volume 34, Issue 11, pp. 4765 - 4780

Journal Article

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