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- W4319778952 abstract "Let Φ:Bn→Bn. A set is the maximal invariant subset of X⊂Bn if it is invariant and it includes any other invariant subset of X. The maximal invariant subsets of X, denoted Xmax1,...,Xmax5, are defined in Section 20.1, and several examples are given in Section 20.2. The fact that Xmax1={μ|μ∈X,∃α∈Πn,Oα(μ)⊂X}, Xmax3=Xmax4={μ|μ∈X,∀α∈Πn,Oα(μ)⊂X}, Xmax5={μ|∃A⊂X,μ∈A and ∀λ∈Bn,Φλ(A)=A} and other important properties of these subsets are presented in Section 20.3. In Section 20.4 we analyze the situation of Xmax1, ...,Xmax5 when the orbit is a nullcline. Section 20.5 points out that the isomorphisms of flows bring maximal invariant subsets in maximal invariant subsets. In Section 20.6 we present the relation between the sets Xmax,Φk and Ymax,Γk, k∈{1,...,4} when Φ is a subsystem of Γ:Bn+m→Bn+m; in Section 20.7, given the systems Φ:Bn→Bn, Ψ:Bm→Bm, we present the relation between Xmax,Φk,Ymax,Ψk and (X×Y)max,Φ×Ψk, k∈{1,...,5}." @default.
- W4319778952 created "2023-02-11" @default.
- W4319778952 creator A5033099994 @default.
- W4319778952 date "2023-01-01" @default.
- W4319778952 modified "2023-09-26" @default.
- W4319778952 title "Maximal invariant subset" @default.
- W4319778952 doi "https://doi.org/10.1016/b978-0-32-395422-8.00026-x" @default.
- W4319778952 hasPublicationYear "2023" @default.
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