Difference between revisions of "File:Exotica1.png"

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{{oq|Exotica1.png|Exotica1.png ‎(630 × 475 pixels, file size: 7 KB, MIME type: image/png)}}
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Exotics, figure for the book «[[Supoerfuncitons]]»; the Russian version is entitled «[[Суперфункции]]».
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This image is used as FIg.10.1 at page 127 of book «[[Суперфункции]]», 2014
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(in Russian) <ref>
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http://mizugadro.mydns.jp/BOOK/202.pdf
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Дмитрий Кузнецов. [[Суперфункции]]. [[Lambert Academic Publishing]] 2014.
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Нецелые итерации голоморфных функций.
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[[Тетрация]] и другие [[суперфункции]. Формулы,
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алгоритмы, графики и комплексные карты.
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</ref>.
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This image is used as Fig.10.2 at page 118 of book
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«[[Superfunctions]]», 2020 <ref>
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https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas,algorithms,tables,graphics - 2020/7/28
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</ref><ref>https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas, algorithms, tables, graphics. Publisher: [[Lambert Academic Publishing]].
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</ref>
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<br>
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in order to remind that is exotics.<br>
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There is very low probability to meet at a street a dog with 6 legs, or a bird with 2 heads or a
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transfer function \(T\) such that has a fixed point \(L\), id est, \(T(L)\!=\!L\),
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but \(\ T'(L)\!=\!1 \ \)
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and therefore the formulas from the Chapter 6 of that book for the [[Regular iteration]]
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are difficult to apply "as is", while \(T'(L)\!-\!1 \) appear in the denominator.
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The similar problem should takes place if \(T'(L)\!=\!0 \); it also appears in the denominator.
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All these cases are qualified as "exotic".
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Perhaps, it is not so easy to deal with animals shown in the picture (it is difficult to find such an animal), but the exotic [[transfer function]]s happened to be pretty doable.
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Several examples are considered in book «[[Superfunctions]]».
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==References==
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{{ref}}
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{{fer}}
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==Keywords==
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«[[1986.04.26.Чернобыльская катастрофа]]»,
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«[[Base e1e]]»,
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«[[Exotic iterations]]»,
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«[[Fixed pount]]»,
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«[[Regular iteraiton]]»,
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«[[Superfunctions]]»,
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«[[Transfer function]]»,
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«[[Притчи]]»,
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«[[Суперфункции]]»,
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[[Category:Book]]
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[[Category:BookDraw]]
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[[Category:Draw]]
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[[Category:Superfunctions]]

Latest revision as of 15:58, 23 August 2025


Exotics, figure for the book «Supoerfuncitons»; the Russian version is entitled «Суперфункции».

This image is used as FIg.10.1 at page 127 of book «Суперфункции», 2014 (in Russian) [1].

This image is used as Fig.10.2 at page 118 of book «Superfunctions», 2020 [2][3]
in order to remind that is exotics.
There is very low probability to meet at a street a dog with 6 legs, or a bird with 2 heads or a transfer function \(T\) such that has a fixed point \(L\), id est, \(T(L)\!=\!L\), but \(\ T'(L)\!=\!1 \ \) and therefore the formulas from the Chapter 6 of that book for the Regular iteration are difficult to apply "as is", while \(T'(L)\!-\!1 \) appear in the denominator. The similar problem should takes place if \(T'(L)\!=\!0 \); it also appears in the denominator. All these cases are qualified as "exotic".

Perhaps, it is not so easy to deal with animals shown in the picture (it is difficult to find such an animal), but the exotic transfer functions happened to be pretty doable. Several examples are considered in book «Superfunctions».

References

  1. ↑ http://mizugadro.mydns.jp/BOOK/202.pdf Дмитрий Кузнецов. Суперфункции. Lambert Academic Publishing 2014. Нецелые итерации голоморфных функций. Тетрация и другие [[суперфункции]. Формулы, алгоритмы, графики и комплексные карты.
  2. ↑ https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics - 2020/7/28
  3. ↑ https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas, algorithms, tables, graphics. Publisher: Lambert Academic Publishing.

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