Article
Mathematics, Applied
Yujun Ju, Qigui Yang
Summary: This paper studies the dynamical properties of Pesin topological entropy for nonautonomous dynamical systems proposed by Li (2015), showing that the box dimension of any subset multiplied by the logarithm of the expanding or Lipschitz constant L provides lower and upper bounds of the corresponding Pesin topological entropies.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Chang -Bing Li, Yuan -Ling Ye
Summary: In this paper, we study the distance entropy, Bowen topological entropy, and the classical topological entropy of nonautonomous dynamical systems. We show that these entropies are equivalent under the condition of weak mixing. Furthermore, we investigate the relationship between distance entropy and Hausdorff dimension in detail.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Hua Shao
Summary: This paper focuses on properties, calculations, and estimations of topological entropy for a nonautonomous dynamical system (X, f0,infinity) generated by a sequence of continuous self-maps f0,infinity = {fn}infinity n=0 on a compact uniform space X. The study proves that (X, f0,infinity) and its k-th product system have the same entropy. It also establishes the equivalence of the entropy of (X, f0,infinity) with its n-th compositions system and the entropy of f0,infinity restricted to its non-wandering set in the case of equi-continuity. Additionally, the paper demonstrates that the entropy of (X, f0,infinity) is less than or equal to that of its limit system (X, f) when f0,infinity converges uniformly to f. Moreover, it reveals that two topologically equi-semiconjugate systems have the same entropy if the equi-semiconjugacy is finite-to-one. Finally, the study provides estimations of upper and lower bounds of entropy for an invariant subsystem of a coupled-expanding system associated with a transition matrix.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Bin Zhang, Lei Liu
Summary: This article focuses on the study of the Bowen topological entropy for nonautonomous dynamical systems, extending the classical definition. The authors demonstrate that the Bowen topological entropy can be determined by the local entropies of measures for nonautonomous dynamical systems, which expands upon the findings of Ma and Wen.
Article
Mathematics
M. Abu-Saleem, Omar Almallah
Summary: This paper aims to deduce the relationship between topology and algebra from the perspectives of geometry and dynamical systems. It introduces the concept of dynamical manifolds associated with a time parameter, and derives topological dynamics on the fundamental group from the chain of dynamical maps on a dynamical manifold. The use of commutative diagrams as chains of dynamical manifolds helps in understanding how manifolds change in a dynamical system viewed through the fundamental group.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Lei Liu, Cao Zhao
Summary: This paper focuses on studying the Bowen polynomial entropy for nonautonomous dynamical systems, which extends the classical definition of Bowen topological entropy. We establish a variational principle for polynomial entropy on compact subsets in the context of nonautonomous dynamical systems, and show that the Bowen topological entropy can be determined by the local entropies of measures for nonautonomous dynamical systems, extending the result of Ma and Wen [33].
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Devender Kumar, Ruchi Das
Summary: This paper studies topological equicontinuity, topological uniform rigidity, and their properties. For a dynamical system on a compact T3 space, the relationships among the set of recurrent points, non-wandering points, and the intersection of all iterations' range sets are studied. The topological version of uniform rigidity is defined, and it is shown that a dynamical system is topologically uniformly rigid if it satisfies certain conditions. Moreover, it is proven that a topologically uniformly rigid dynamical system on a compact Hausdorff space has zero topological entropy, and necessary examples and counterexamples are provided.
Article
Mathematics
Chunlin Liu, Xiaomin Zhou
Summary: The notion of topological entropy dimension is introduced to measure the complexity of entropy zero systems in a Z2-topological dynamical system. The directional entropy dimension is considered in a new way, and the directional entropy dimension tuples and sets are introduced. Equivalent definitions of directional entropy dimension are provided by considering the dimension or density of special sequences encountered by directional entropy. Applications include the discussion of disjointness between entropy zero Z2-systems involving directional entropy dimension.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Xiao Jun Huang, Bin Zhu
Summary: In this paper, the relationship between multi-sensitivity and topological maximal sequence entropy of dynamical systems under general group action is studied. The consistency of multi-sensitivity is discussed for a dynamical system (G curved right arrow X) and its hyperspace dynamical system G curved right arrow K (X). The relationship between the multi-sensitivity of two dynamical systems and the multi-sensitivity of their product space dynamical system is also researched.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
Article
Mathematics, Applied
Ermerson Araujo
Summary: The goal of this article is to study how combinatorial equivalence implies topological equiconjugacy. For that, kneading sequences for a particular class of nonautonomous discrete dynamical systems are introduced, and it is shown that these sequences are a complete invariant for topological equiconjugacy classes.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Ruifeng Zhang, Jianghui Zhu
Summary: In this paper, the concepts of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems are introduced. Furthermore, the variational principle between packing topological entropy and measure-theoretical upper entropy is established.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Engineering, Multidisciplinary
M. C. Shanmukha, Sokjoon Lee, A. Usha, K. C. Shilpa, Muhammad Azeem
Summary: Graph theory is widely used in chemistry, pharmacy, communication, maps, and aeronautical fields. Molecules are modeled as graphs to study their properties. This article aims to apply graph theory to the structures of benzenoid hydrocarbons and graphenylene. Topological indices are used to examine the correlation between chemical structures and physical, chemical properties. Novel entropy descriptors are introduced and linear regression models are used to analyze the physico-chemical properties of these compounds.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Applied
Hua Shao
Summary: This article presents the nonautonomous dynamical system and the fuzzified system of continuous self-maps, and proves the relationships between various properties.
TOPOLOGY AND ITS APPLICATIONS
(2023)
Article
Mathematics, Applied
Khadija Ben Rejeb
Summary: This study focuses on abelian nonautonomous dynamical systems F on compact spaces X that are transitive, extending results from a previous study. It is shown that such F must exhibit either pointwise sensitivity or uniform rigidity and almost equicontinuity. Additionally, it is proven that the equicontinuity points of F, when having nonempty interior, coincide with the transitive points, and F is equicontinuous if and only if it is minimal. The study also delves into chaos for F, establishing that Devaney chaos implies Li-Yorke chaos.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
David Cheban
Summary: This paper focuses on the dynamics of one-dimensional monotone nonautonomous (cocycle) dynamical systems. It provides a description of the structures of their invariant sets, omega limit sets, Bohr/Levitan almost periodic and almost automorphic motions, global attractors, pinched and minimal sets. An application of these general results is made to scalar differential and difference equations.
SCIENCE CHINA-MATHEMATICS
(2023)
