Limit Sets Research Articles

Factors associated with physical and psychological wellness of American adults with asthma

Objective: The study objective was to investigate the factors associated with the physical and psychological wellness of United States (US) adults with asthma.Methods: This cross-sectional analysis used a sample of 2329 US adults with asthma in the 2021 Medical Expenditure Panel Survey data. A logistic regression model investigated the association of the following factors and the dependent variables (physical wellness and psychological wellness): age, sex, race, ethnicity, education, employment, healthcare provision, marriage, income, regular physical activity, current smoker, pain, and limitations. Nationally representative estimates were produced through a weighted analysis. The data structure was maintained using cluster and strata variables. The alpha limit was 0.05.Results: Factors associated with higher odds of reporting good physical wellness included: private (versus no) healthcare provision (odds ratio [OR] = 2.63, 95% confidence interval [CI] = 1.10–6.26), good (versus poor) psychological wellness (OR = 6.83, 95% CI = 4.35–10.72), regular (versus no regular) physical activity (OR = 2.18, 95% CI = 1.42–3.34), little/moderate (versus quite a bit/extreme) pain (OR = 3.51, 95% CI = 2.38–5.15) and no (versus any) limitation (OR = 3.73, 95% CI = 2.30–6.06). In the psychological wellness model, those aged ≥70 (OR = 6.18, 95% CI = 2.72–14.07), 60–69 (OR = 4.64, 95% CI = 2.13–10.10), and 50–59 (OR = 4.96, 95% CI = 2.24–11.02) versus those aged 18–29, and good (versus poor) physical wellness (OR = 6.89, 95% CI = 4.34–10.94) were associated with higher odds of reporting good versus poor psychological wellness.Conclusion: These results may be helpful at targeting resources to optimize the wellness of US adults with asthma. Additional studies are needed to determine any temporal associations between these findings.

Effectiveness of Animated Video Education in Improving Knowledge and Attitudes towards Primary Dysmenorrhea Management among Students in Surabaya

The incidence of menstruation indicates that physical maturity and the reproductive system have occurred in women. One of the disorders during menstruation is menstrual pain or primary dysmenorrhea. If primary dysmenorrhea is not treated, it will cause painful effects to reduce learning concentration which affects learning ability. Therefore, efforts that can be made to improve students' knowledge and attitudes in handling primary dysmenorrhea are by providing animated video education that is able to bring adolescents into an atmosphere of joy and joy. This study used the Pre-Experimental One Group Pretest-Posttest Design research design. The population is class X students at SMK Tri Guna Bhakti Surabaya. The research sample was 45 female students using random sampling techniques. Data collection used questionnaires and observation sheets, while data analysis used the Wilcoxon Signed Rank Test. The results of the Wilcoxon Signed Rank Test statistical test show a knowledge p value of 0.000 and an attitude of 0.001 which is less than the alpha limit determined by the researcher which is 0.05. There is an influence of animated video media on increasing the knowledge and attitudes of grade X students at SMK Tri Guna Bhakti Surabaya after being given an educational intervention for handling primary dysmenorrhea.

Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed

Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to S0 and S± is also proven with the aid of a Lyapunov function and the definitions of both the α-limit set and ω-limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc.

Assouad type dimensions of infinitely generated self-conformal sets

We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of sets. Under natural separation conditions, we prove a formula for the Assouad dimension and prove sharp bounds for the Assouad spectrum in terms of the Hausdorff dimension of the limit set and dimensions of the set of fixed points of the contractions. The Assouad spectra of the family of examples which we use to show that the bounds are sharp display interesting behaviour, such as having two phase transitions. Our results apply in particular to sets of real or complex numbers which have continued fraction expansions with restricted entries, and to certain parabolic attractors.

On limit sets of simplest skew products defined on multidimensional cells

The purpose of this work is to describe two important types of limit sets of the most simple skew products of interval maps, the phase space of each of which is a compact n-dimensional cell (n ≥ 2): firstly, a non-wandering set and, secondly, ω-limit sets of trajectories. Methods. A method for investigating of a nonwandering set (new even for the two-dimensional case) is proposed, based on the use of the concept of C0-Ω-blow up in continuous closed interval maps, and the concept of C0-Ω-blow up introduced in the work in the family of continuous fibers maps. To describe the ω-limit sets, the technique of special series constructed for the trajectory and containing an information about its asymptotic behavior is used. Results. A complete description is given of the nonwandering set of the continuous simplest skew product of the interval maps, that is, a continuous skew product on a compact n-dimensional cell, the set of (least) periods of periodic points of which is bounded. The results obtained in the description of a nonwandering set are used in the study of ω-limit sets. The paper describes a topological structure of ω-limit sets of the maps under consideration. Sufficient conditions have been found under which the ω-limit set of the trajectory is a periodic orbit, as well as the necessary conditions for the existence of one-dimensional ω-limit sets. Conclusion. Further development of the C0-Ω-blow up technique in the family of maps in fibers will allow us to describe the structure of a nonwandering set of skew products of one-dimensional maps, in particular, with a closed set of periodic points defined on the simplest manifolds of arbitrary finite dimension. Further development of the theory of special divergent series constructed in the work will allow us to proceed to the description of ω-limit sets of arbitrary dimension d, where 2 ≤ d ≤ n - 1, n ≥ 3, in the simplest skew products.

Forest Dynamics and the Analysis of a Reaction-Diffusion Forest Model

In this research, we study the dynamics of ecological models governed by differential equations. Ecology provides insight into the interaction between forest organisms, and interrelated processes regarding flora, fauna, and numerous other species. In particular, the results support population thresholds necessary for survival in some instances. Subsequently, we explore the response of mangroves of different regions to natural calamities and man-made disasters. A reaction-diffusion model has been developed to see the dynamics of the tidal woods and wetlands. Sundarbans, the largest mangrove of Bangladesh, are victim to a vast amount of hazardous events. This mathematical study of mangroves is unprecedented in such a manner. Furthermore, we continue the study of a forest ecosystem governed by an age-structured parabolic-ordinary system. We study some properties of an abstract parabolic equation, the dynamical system, and the limit sets. The model demonstrates a Lyapunov function which denotes some vital properties of the limit sets. GANIT J. Bangladesh Math. Soc. 43.1 (2023) 26- 36

Almost Periodic Functions: Their Limit Sets and Various Applications

Almost Periodic Functions: Their Limit Sets and Various Applications

Minimality and distributional chaos in triangular maps

The result of this paper contributes to the classification of triangular maps of the square with zero topological entropy stated by A. N. Sharkovsky in the 1980s. The problem was if a triangular map of the square such that its any ω-limit set contains unique minimal set can be distributionally chaotic. So far such result was disproved only for the class of triangular maps non-decreasing on fibres [L. Paganoni, J. Smítal, Strange distributionally chaotic triangular maps, Chaos Solitons Fractals 26(2) (2005), pp. 581–589]. In this paper, we solve the problem in negative for all triangular maps of the square, correcting the original result from Balibrea and Smítal [Strong distributional chaos and minimal sets, Topology appl. 156 (2009), pp. 1673–1678].

Asymptotically almost periodic points and sensitivity of continuous maps

In this paper, the sensitivity of continuous self-maps is studied, containing transitive maps and non-transitive maps. The concepts of asymptotically almost periodic points and uniformly segment-recurrent points are raised, which are generalizations of the concept of almost periodic points. The concept of allured sets is also introduced, which is the opposite concept of ω-limit sets. By means these concepts, we obtain some conditions for a continuous map f from a metric space X to itself to be sensitive. Our results are generalizations of the main theorems given in [2,4,8,15,24,27].

Global vs Blow-Up Solutions and Optimal Threshold for Hyperbolic ODEs with Possibly Singular Nonlinearities

We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the stationary problem. Then, for small value of the perturbation parameter as well as initial value, we establish the existence of a global solution by means of the Lyapunov function and we show that the omega limit set consists of a solution to the stationary problem. For strong perturbations or large initial values, we show that the solution blows up. Finally, we discuss the relationship between upper bounds of the perturbation parameter for the existence of time-dependent and stationary solutions, for which we establish an optimal threshold.

The Limit Set for Representations of Discrete Subgroups of $$\text {PU}(1,n)$$ by the Plücker Embedding

AbstractLet $$\Gamma $$ Γ be a discrete subgroup of $$\text {PU}(1,n)$$ PU ( 1 , n ) . In this work, we look at the induced action of $$\Gamma $$ Γ on the projective space $$\mathbb {P}(\wedge ^{k+1}\mathbb {C}^{n+1})$$ P ( ∧ k + 1 C n + 1 ) by the Plücker embedding, where $$\wedge ^{k+1}$$ ∧ k + 1 denotes the exterior power. We define a limit set for this action called the k-Chen-Greenberg limit set, which extends the classical definition of the Chen-Greenberg limit set $$L(\Gamma )$$ L ( Γ ) , and we show several of its properties. We prove that its Kulkarni limit set is the union taken over all $$p\in L(\Gamma )$$ p ∈ L ( Γ ) of the projective subspace generated by all k-planes that contain p or are contained in $$p^{\perp }$$ p ⊥ via the Plücker embedding. We also prove a duality between both limit sets.

Robust limit cycle control for finite-time generation of sustained oscillations in nonlinear systems with mixed dead-zone and saturation

This paper suggests a novel limit cycle control technique, based on the finite-time stability scheme, for producing sustained oscillations in a class of nonlinear complex systems. The considered systems are constrained to input dead-zone and saturation simultaneously and suffer from non-vanishing perturbations due to model uncertainties, and external disturbances. For this purpose, an innovative sliding manifold is proposed based on the topology of the wanted limit cycle which provides the conditions for developing the finite time stability concept for limit sets. With the aid of the finite-time command filter and the cooperation of the sliding mode control (SMC) method with the backstepping technique, a robust controller is constructed which guarantees the finite-time convergence of phase trajectories of the closed-loop system toward the wanted limit cycle. This leads to the creation of sustained oscillations, with the desirable amplitude and frequency, in the system's output. The stability analysis is proved based on the Lyapunov approach through the set stability concept. Finally, the effectiveness of the suggested methodology is confirmed by a variety of simulations.

Dichotomy and Measures on Limit Sets of Anosov Groups

Abstract Let $G$ be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup $\Gamma <G$, we show that a $\Gamma $-conformal measure is supported on the limit set of $\Gamma $ if and only if its dimension is $\Gamma $-critical. This implies the uniqueness of a $\Gamma $-conformal measure for each critical dimension, answering the question posed in our earlier paper with Edwards [13]. We obtain this by proving a higher rank analogue of the Hopf–Tsuji–Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.

ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations

In this paper, we investigate the qualitative behavior of an evolutionary problem consisting of a hyperbolic dissipative equation whose trajectories undergo instantaneous impulsive discontinuities at the moments when the energy functional reaches a certain threshold value. The novelty of the current study is that we consider the case in which the entire infinite-dimensional phase vector undergoes an impulsive disturbance. This substantially broadens the existing results, which admit discontinuities for only a finite subset of phase coordinates. Under fairly general conditions on the system parameters, we prove that such a problem generates an impulsive dynamical system in the natural phase space, and its trajectories have nonempty compact ω-limit sets.

Global Dynamics of Planar Piecewise Linear Inelastic systems having straight lines as switching manifolds

In this paper we classify the phase portrait and the limit sets of a special class of piecewise smooth vector fields in the plane with different configurations of straight lines as switching manifolds. We study the behavior at infinity through a Poincaré compactification as well as the relations between canonical regions and vector fields which are defined over the switching regions. Results addressing the global behavior of trajectories, tangency points, vector fields over the switching manifolds, and equilibrium and pseudo-equilibrium points at the finite and the infinite part are stated. In particular, we prove the existence of 123 distinct phase portraits for the class of piecewise smooth vector fields that we consider.

A hybrid model of population dynamics with refuge-regime: regularization and self-organization

A mathematical model of the dynamics of the predator and prey populations in the form of a hybrid dynamical system consisting of two two-dimensional systems switching between each other is proposed. Switching of the systems allows us to reproduce a special refuge-regime when the prey number is very small and predators have complications to find preys. The sliding modes are studied using Filippov approach. Regularization of the system by using two switching lines to avoid chattering is provided. For the regularized model the limit sets are established. A scenario of the system self-organization preventing the unbounded populations' growth is proposed. A sensitivity study is carried out with respect to a parameter defining the switching lines. An important result of the research is that sufficiently small changing of the switching lines does not change the qualitative behavior of the system.

Hausdorff dimension of limit sets for projective Anosov representations

Hausdorff dimension of limit sets for projective Anosov representations

Dynamical properties of convex cocompact actions in projective space

AbstractWe give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups that are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.

A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra

The Sullivan dictionary provides a beautiful correspondence between Kleinian groups acting on hyperbolic space and rational maps of the extended complex plane. We focus on the setting of geometrically finite Kleinian groups with parabolic elements and parabolic rational maps. In this context an especially direct correspondence exists concerning the dimension theory of the associated limit sets and Julia sets. In recent work we established formulae for the Assouad type dimensions and spectra for these fractal sets and certain conformal measures they support. This allows a rather more nuanced comparison of the two families in the context of dimension. In this expository article we discuss how these results provide new entries in the Sullivan dictionary, as well as revealing striking differences between the two families.

Nonisolated Limit Sets for Some Hydrodynamic Systems with Limited Excitation

Nonisolated Limit Sets for Some Hydrodynamic Systems with Limited Excitation