Kato's chaos created by quadratic mappings associated with spherical orthotomic curves
Journal of Singularities, Tome 21 (2020), pp. 205-211
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In this paper, we first show that for a given generic spherical curve γ: I -> S^n and a generic point P in S^n, the spherical orthotomic curve relative to γ and P naturally yield a simple quadratic mapping Φ_P: R^{n+1}-> R^{n+1}. Since S^n is compact and Φ_P|_{S^n}: S^n -> S^n is the spherical counterpart of the trivial expanding mapping x -> 2x, it is natural to expect a chaotic behavior for the iteration of Φ_P|_{S^n}. Accordingly, we show that Φ_P|_{S^n} (and incidentally Φ_P|_{D^{n+1}} as well) actually creates Kato's chaos. Therefore, by investigating spherical orthotomic curves, %it turns out that an example of singular quadratic mapping creating Kato's chaos is naturally obtained.
@article{10_5427_jsing_2020_21l,
author = {Takashi Nishimura},
title = {Kato's chaos created by quadratic mappings associated with spherical orthotomic curves},
journal = {Journal of Singularities},
pages = {205--211},
publisher = {mathdoc},
volume = {21},
year = {2020},
doi = {10.5427/jsing.2020.21l},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21l/}
}
TY - JOUR AU - Takashi Nishimura TI - Kato's chaos created by quadratic mappings associated with spherical orthotomic curves JO - Journal of Singularities PY - 2020 SP - 205 EP - 211 VL - 21 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21l/ DO - 10.5427/jsing.2020.21l ID - 10_5427_jsing_2020_21l ER -
%0 Journal Article %A Takashi Nishimura %T Kato's chaos created by quadratic mappings associated with spherical orthotomic curves %J Journal of Singularities %D 2020 %P 205-211 %V 21 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21l/ %R 10.5427/jsing.2020.21l %F 10_5427_jsing_2020_21l
Takashi Nishimura. Kato's chaos created by quadratic mappings associated with spherical orthotomic curves. Journal of Singularities, Tome 21 (2020), pp. 205-211. doi: 10.5427/jsing.2020.21l
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