论文标题
紧凑型公制空间上单侧动力系统的takens型重建定理
Takens-type reconstruction theorems of one-sided dynamical systems on compact metric spaces
论文作者
论文摘要
重建定理涉及由映射$ t：x \至紧凑型公制空间$ x $的X $给出的动态系统，可观察到的$ f：x \ to \ r $从$ x $到实线$ \ r $。在1981年，通过使用惠特尼的嵌入定理，塔克斯证明，如果$ t：m \ to m $ to m $是紧凑的平滑流形$ m $，带有$ \ dim m = d $的差异性，对于通用$（t，f）$ $（ft^j（x））_ {j = 0}^{2d} $，此外，在2002年，Takens在2002年证明了内态性的广义版本。 在自然科学和物理工程中，分形集和更复杂的空间以及数学的重要性增加了，许多拓扑和动力学特性以及对此类空间的随机分析进行了研究。在本文中，通过使用某些拓扑方法，我们扩展了Takens的重建平滑歧管的重建定理，以重建一类动力学系统，用于一系列紧凑型度量空间，其中包含PL-manifolds，分支歧管，分支歧管和一些分形集合，例如。 Menger流形，Sierpiński地毯和Sierpiński垫圈和树突等。
The reconstruction theorem deals with dynamical systems that are given by a map $T:X\to X$ of a compact metric space $X$ together with an observable $f:X \to \R$ from $X$ to the real line $\R$. In 1981, by use of Whitney's embedding theorem, Takens proved that if $T:M\to M$ is a diffeomorphism on a compact smooth manifold $M$ with $\dim M=d$, for generic $(T,f)$ there is a bijection between elements $x \in M$ and corresponding sequence $(fT^j(x))_{j=0}^{2d}$, and moreover, in 2002 Takens proved a generalized version for endomorphisms. In natural sciences and physical engineering, there has been an increase in importance of fractal sets and more complicated spaces, and also in mathematics, many topological and dynamical properties and stochastic analysis of such spaces have been studied. In the present paper, by use of some topological methods we extend the Takens' reconstruction theorems of compact smooth manifolds to reconstruction theorems of one-sided dynamical systems for a large class of compact metric spaces, which contains PL-manifolds, branched manifolds and some fractal sets, e.g. Menger manifolds, Sierpiński carpet and Sierpiński gasket and dendrites, etc.
