Abstract
The Maunder butterfly pattern is the most complete spatial-temporal representation of observed changes in solar activity in the 11-year cycle over a period of 12–24 cycle. The well-known empirical relation is used to transform Greenwich sunspot areas into magnetic flux, and the distances between the butterfly wings are then calculated with the Fisher–Rao metric. We found that the similarities or differences in the patterns of the individual butterfly wings in this metric are approximately the same for each hemisphere. The wings were the closest for a sequence of strong cycles, while there is a tendency for a series of weak cycles to form cycles in pairs with the implementation of an analog of the Gnevyshev–Olya rule.
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Notes
Density vectorized in this way is called the persistent image.
For the pair of real \({{L}_{2}}\) functions \(f\) and \(g\), this product is defined as \(\left( {f,g} \right) = \int {f\left( x \right)g\left( x \right)dx} .\)
The normalized vector space with the metric (2) is induced by the norm.
That is, each point enters with a weight that determines pdf.
They are sometimes called half densities.
T. expanding the matrix in the row “snake”.
Local diffeomorphism.
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ACKNOWLEDGMENTS
The authors thank the anonymous reviewer for comments.
Funding
This work was supported by grant AP05134227 (Kazakhstan), and the work of D.M. Volobuev was partially supported by the Russian Foundation for Basic Research (project no. 19-02-00088).
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Volobuev, D.M., Makarenko, N.G. & Knyazeva, I.S. Features of Spatiotemporal Clustering in a Maunder Butterfly Diagram. Geomagn. Aeron. 59, 1036–1041 (2019). https://doi.org/10.1134/S0016793219080255
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DOI: https://doi.org/10.1134/S0016793219080255