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- W4317464057 abstract "This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems $(X,f)$ and $(Y,g)$. More precisely, given $x_1,ldots, x_n subset X$ and $y_1,ldots,y_n subset Y$ such that $x_{i+1} = f(x_i)$ and $y_{i+1} = g(y_i)$ as well as $h: X rightarrow Y$, we deliver a number of tests to check if $f$ and $g$ are topologically conjugated via $h$. The values of the tests are close to zero for conjugated systems and large for systems that are not conjugated. Convergence of the test values, in case when sample size goes to infinity, is established. A number of numerical examples indicating scalability and robustness of the methods are given. In addition, we show how the presented method specialize to a test of sufficient embedding dimension in Takens' embedding theorem. Our methods also apply to the situation when we are given two observables of deterministic processes, of a form of one or higher dimensional time-series. In this case, their similarity can be accessed by comparing the dynamics of their Takens' reconstructions." @default.
- W4317464057 created "2023-01-20" @default.
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- W4317464057 date "2023-01-17" @default.
- W4317464057 modified "2023-10-13" @default.
- W4317464057 title "Testing topological conjugacy of time series" @default.
- W4317464057 doi "https://doi.org/10.48550/arxiv.2301.06753" @default.
- W4317464057 hasPublicationYear "2023" @default.
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