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Representation up to Homotopy and Hom-Lie Algebroid Modules 到同伦和同李代数模的表示
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2020-01-02 DOI: 10.1080/1726037X.2020.1788817
S. Merati, M. R. Farhangdoost, A.R. Attari Polsangi
{"title":"Representation up to Homotopy and Hom-Lie Algebroid Modules","authors":"S. Merati, M. R. Farhangdoost, A.R. Attari Polsangi","doi":"10.1080/1726037X.2020.1788817","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1788817","url":null,"abstract":"Abstract In this paper we introduce the concept of hom-Lie algebroid modules and hom-Lie algebroids. Then we show the correspondence between hom-Lie algebroid modules and representation up to homotopy of hom-Lie algebroids. Because of the effective role of representation theory and Lie algebraic structures in particle physics, we show the correspondence between bi-graded hom-Lie algebraic modules and hom-Lie algebraist. At the end, we study some properties of representation up to homotopy, using the language of hom-Lie algebroid modules.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"27 - 37"},"PeriodicalIF":0.9,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1788817","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46693933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dynamics Of Frw Type Kaluza-Klein Mhrde Cosmological Model In Self-Creation Theory 自我创造理论中Frw型Kaluza-Klein Mhrde宇宙学模型的动力学
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2020-01-02 DOI: 10.1080/1726037X.2020.1774158
T. Vinutha, K. S. Sri Kavya
{"title":"Dynamics Of Frw Type Kaluza-Klein Mhrde Cosmological Model In Self-Creation Theory","authors":"T. Vinutha, K. S. Sri Kavya","doi":"10.1080/1726037X.2020.1774158","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1774158","url":null,"abstract":"ABSTRACT In this work, we have studied Friedmann–Robertson–Walker type Kaluza–Klein universe filled with pressureless matter and modified holographic Ricci dark energy in the frame work of Barber’s self-creation theory. While solving field equations we have considered hybrid expansion law of average scale factor. Also we have studied differences between open, flat and closed models. We have calculated some physical properties such as deceleration parameter(q), EoS parameter(ωde ), spatial volume(V ), expansion scalar(θ). The physical and geometrical aspects of the statefinder parameters(r, s) and ωde − ω ′ de plane are also discussed. In ω de− ω ′ de plane discussion we have observed that the flat model lies in freezing region and the closed model lies in thawing region. Also we have observed that for flat model ωde crosses the phantom divide line( i.e. ωde = -1) and shows quintom like behavior. Among the three models the flat model is in good agreement with recent observational data.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"111 - 129"},"PeriodicalIF":0.9,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1774158","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44499644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Characteristic of pointwise-recurrent maps on a dendrite 枝晶上逐点递归映射的特征
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2020-01-02 DOI: 10.1080/1726037X.2020.1779971
G. Su, T. Sun, Caihong Han, Bin Qin
{"title":"Characteristic of pointwise-recurrent maps on a dendrite","authors":"G. Su, T. Sun, Caihong Han, Bin Qin","doi":"10.1080/1726037X.2020.1779971","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1779971","url":null,"abstract":"Abstract Let f be a continuous map on a dendrite D with f (D) = D. Denote by R(f ) and AP (f ) the set of recurrent points and the set of almost periodic points of f , respectively, and denote by ω(x, f ), Λ(x, f ), Γ(x, f ) and Ω(x, f ) the set of ω-limit points, the set of α-limit points, the set of γ-limit points and the set of weak ω-limit points of x under f , respectively. In this paper, we show that the following statements are equivalent: (1) D = R(f ). (2) D = AP (f ). (3) Ω(x, f ) = ω(x, f ) for any x ∈ D. (4) Ω(x, f ) = Γ(x, f ) for any x ∈ D. (5) f is equicontinuous. (6) [c, d] ⊄ Ω(x, f ) for any c, d,x ∈ D with c ≠ (7) Ω(x, f ) is minimal for any x ∈ D. (8) Card(Λ − 1(x, f ) ∩ (D−End(D))) < ∞ for any x ∈ D, where Λ − 1(x, f ) = {y : x ∈ Λ(y, f )}, End(D) is the set of endpoints of D and Card(A) is the cardinal number of set A. (9) If x ∈ Λ(y, f ) with x, y ∈ D, then y ∈ ω(x, f ). (10) Map h : x → ω(x, f ) (x ∈ D) is continuous and for any x, y ∈ D with x ∉ ω(y, f ), ω(x, f ) ≠ ω(y, f ). Besides, we also study characteristic of pointwise-recurrent maps on a dendrite with the number of branch points being finite.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"1 - 14"},"PeriodicalIF":0.9,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1779971","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45457373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Submersions of Contact CR-Submanifolds of Generalized Quasi Sasakian Manifolds 广义拟sasaki流形的接触cr -子流形的淹没
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2020-01-02 DOI: 10.1080/1726037X.2020.1796247
M. Siddiqi
{"title":"Submersions of Contact CR-Submanifolds of Generalized Quasi Sasakian Manifolds","authors":"M. Siddiqi","doi":"10.1080/1726037X.2020.1796247","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1796247","url":null,"abstract":"Abstract In this paper, we discuss some properties of almost contact metric submersion of contact CR-submanifolds of generalized quasi-Sasakian manifold and derive some results based on their curvatures’s differential geometry. We also study de-Rham cohomology of CR-submanifold of generalized quasi-Sasakian manifold under the submersion.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"81 - 95"},"PeriodicalIF":0.9,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1796247","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48755785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature 慢不变流形计算的微分几何公式:测地线拉伸和流动曲率
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-12-02 DOI: 10.1080/1726037X.2022.2060909
D. Lebiedz, Johannes Poppe
{"title":"On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature","authors":"D. Lebiedz, Johannes Poppe","doi":"10.1080/1726037X.2022.2060909","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2060909","url":null,"abstract":"Abstract The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many approximation methods exploit the restrictive requirement of an explicit time-scale separation parameter. Most of those methods are also not formulated covariantly, i.e. in terms of tensorial constructions. We propose an intrinsically coordinate-free differential geometric approximation criterion approximating normally attracting invariant manifolds (NAIMs). We translate some ideas behind existing approximation approaches, the stretching based diagnostics (SBD) and the flow curvature method (FCM) to tensors of Riemannian geometry, specifically to spacetime curvature in extended phase space. For that purpose we derive from flow-generating smooth vector fields a metric tensor such that the original dynamical system is a geodesic flow on a Riemannian manifold. We apply the resulting method to test models.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"1 - 32"},"PeriodicalIF":0.9,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44798653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Yamabe Solitons On (LCS) n -Manifolds (LCS) n -流形上的Yamabe孤子
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-09-14 DOI: 10.1080/1726037X.2020.1868100
Soumendu Roy, S. Dey, A. Bhattacharyya
{"title":"Yamabe Solitons On (LCS) n -Manifolds","authors":"Soumendu Roy, S. Dey, A. Bhattacharyya","doi":"10.1080/1726037X.2020.1868100","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1868100","url":null,"abstract":"Abstract The object of the present paper is to study some properties of (LCS) n -manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS) n -manifolds when the soliton becomes steady. Next we have studied some certain curvature conditions of (LCS) n -manifolds admitting Yamabe solitons. Lastly we construct a 3-dimensional (LCS) n -manifold satisfying the results.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"261 - 279"},"PeriodicalIF":0.9,"publicationDate":"2019-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1868100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48580113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Lyapunov Exponents for Quantum Channels: An Entropy Formula and Generic Properties 量子通道的Lyapunov指数:一个熵公式和一般性质
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-08-22 DOI: 10.1080/1726037X.2021.2014635
Jader E. Brasil, J. Knorst, A. Lopes
{"title":"Lyapunov Exponents for Quantum Channels: An Entropy Formula and Generic Properties","authors":"Jader E. Brasil, J. Knorst, A. Lopes","doi":"10.1080/1726037X.2021.2014635","DOIUrl":"https://doi.org/10.1080/1726037X.2021.2014635","url":null,"abstract":"Abstract We denote by Mk the set of k by k matrices with complex entries. We consider quantum channels φL of the form: given a measurable function L: Mk → Mk and a measure µ on Mk we define the linear operator φL : Mk → Mk , by the law ρ → φL (ρ) = ∫ Mk L(v)ρL(v)† dµ(v). In a previous work, the authors show that for a fixed measure µ the Φ-Erg property is generic on the function L (also irreducibility). Here we will show that the purification property is also generic on L for a fixed µ. Given L and µ there are two related stochastic processes: one takes values on the projective space P (ℂ k ) and the other on matrices in Mk . The Φ-Erg property and the purification condition are the nice hypothesis for the discrete time evolution given by the natural transition probability. In this way it will follow that generically on L, if ∫ |L(v)|2 log |L(v)| dµ(v) < ∞, the Lyapunov exponents ∞ > γ 1 ≥ γ 2 ≥ … ≥ γk ≥ −∞ are well defined. In a previous work, the concepts of entropy of a channel and Gibbs channel were presented; and also an example (associated to a stationary Markov chain) in which this definition of entropy (for a quantum channel) matches the Kolmogorov-Shanon definition of entropy. We estimate here the larger Lyapunov exponent for the mentioned example and we show that it is equal to −1/2 h, where h is the entropy of the associated Markov invariant probability.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"155 - 187"},"PeriodicalIF":0.9,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Kaluza Klein Type FRW Cosmological Model With Extended Chaplygin Gas 扩展Chaplygin气体的Kaluza Klein型FRW宇宙学模型
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-07-03 DOI: 10.1080/1726037X.2019.1651491
G. S. Khadekar, N. Ramtekkar
{"title":"Kaluza Klein Type FRW Cosmological Model With Extended Chaplygin Gas","authors":"G. S. Khadekar, N. Ramtekkar","doi":"10.1080/1726037X.2019.1651491","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1651491","url":null,"abstract":"Abstract In this paper we consider the extended Chaplygin gas equation of state as a model of dark energy for which it recovers barotropic fluids with quadratic equation of state. We obtain scale factor dependence energy density and Hubble expansion parameter for particular values of n, m and α. Similarly for arbitrary values of n, m and α we have discuss nature of cosmological parameters such as scale factor, Hubble expansion parameter, time dependent dark energy density and deceleration parameter in the framework of Kaluza Klein type FRW cosmological model. Further, we study stability of the model by using speed of sound and observe that the model is stable at late time.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"149 - 172"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1651491","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43844850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Multifractal Pressure for Countable Markov Shifts 关于可数Markov位移的多重分形压力
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-07-03 DOI: 10.1080/1726037X.2019.1668150
A. Mesón, F. Vericat
{"title":"On a Multifractal Pressure for Countable Markov Shifts","authors":"A. Mesón, F. Vericat","doi":"10.1080/1726037X.2019.1668150","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1668150","url":null,"abstract":"Abstract In a recent article [J. d' Analyse Math 131, 207, 2017], Olsen intoduced a generalized notion of multifractal pressure, and also a multifractal dynamical zeta function, which essentilly consists in considering not all configurations, but those which are ”multifractally relevant”. In this way more precise information about the multifractal spectrum analyzed is encoded by the multifractal pressure and the multifratcal zeta function. He applied the theory for dynamical systems modelled by finite alphabet shifts, in particular for self conformal iterated systems. Here we continue with this line considering dynamical systems given by countable Markov shifts.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"267 - 295"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42576146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Cosmological Application in Kaluza-Klein Theory: Generalized Sudden Singularity Kaluza-Klein理论中的宇宙学应用:广义突发性奇点
IF 0.9
Journal of Dynamical Systems and Geometric Theories Pub Date : 2019-07-03 DOI: 10.1080/1726037X.2019.1668147
Rupali Wanjari, G. S. Khadekar
{"title":"Cosmological Application in Kaluza-Klein Theory: Generalized Sudden Singularity","authors":"Rupali Wanjari, G. S. Khadekar","doi":"10.1080/1726037X.2019.1668147","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1668147","url":null,"abstract":"Abstract In this paper, we considered the cosmological application by taking G and Λ to be a function of t in Kaluza-Klein cosmology. We use the Taylor’s expansion of cosmological function Λ(t), up to the first order of time t and evaluated the cosmological parameters by using the modified equation of state of the form p = −ρ − f (ρ), where f (ρ) = αρ. The analytical properties of R(t), ρ(t) and H(t) are investigated and it is observed that from the solutions of the field equations, the generalized sudden singularity occurs at a finite time in the framework of Kaluza-Klein theory of gravitation.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"205 - 220"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43459556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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