A dynamical approach to the infinitesimal spaces of quasiconformal mappings
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- by Hideki Miyachi PDF
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Abstract:
In this paper, we discuss the structure of the infinitesimal spaces of generic quasiconformal mappings. One of the main results is that for any countable set in the complex plane, the infinitesimal spaces of generic $K$-quasiconformal mappings at any point in the set is the totality of $K$-quasiconformal mappings.References
- David B. Ellis, Robert Ellis, and Mahesh Nerurkar, The topological dynamics of semigroup actions, Trans. Amer. Math. Soc. 353 (2001), no. 4, 1279–1320. MR 1806740, DOI 10.1090/S0002-9947-00-02704-5
- A. Fletcher and B. Wallis, The orbits of generalized derivatives, arXiv:1706.04111 (2017).
- V. Ya. Gutlyanskiĭ, O. Martio, V. I. Ryazanov, and M. Vuorinen, Infinitesimal geometry of quasiregular mappings, Ann. Acad. Sci. Fenn. Math. 25 (2000), no. 1, 101–130. MR 1737430
- Bogdan Bojarski, Vladimir Gutlyanskii, Olli Martio, and Vladimir Ryazanov, Infinitesimal geometry of quasiconformal and bi-Lipschitz mappings in the plane, EMS Tracts in Mathematics, vol. 19, European Mathematical Society (EMS), Zürich, 2013. MR 3088451, DOI 10.4171/122
- N. Bourbaki, Éléments de mathématique. I: Les structures fondamentales de l’analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1045, Hermann, Paris, 1958 (French). Deuxième édition revue et augmentée. MR 0173226
- Grant Cairns, Alla Kolganova, and Anthony Nielsen, Topological transitivity and mixing notions for group actions, Rocky Mountain J. Math. 37 (2007), no. 2, 371–397. MR 2333376, DOI 10.1216/rmjm/1181068757
- Vladimir I. Ryazanov and Matti K. Vuorinen, On Belinskii conformality in countable sets of points, Proc. Amer. Math. Soc. 129 (2001), no. 10, 3049–3056. MR 1840111, DOI 10.1090/S0002-9939-01-05932-9
Additional Information
- Hideki Miyachi
- Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan
- Address at time of publication: School of Mathematics and Physics, College of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan
- MR Author ID: 650573
- Email: miyachi@se.kanazawa-u.ac.jp
- Received by editor(s): October 22, 2017
- Received by editor(s) in revised form: April 10, 2018
- Published electronically: October 3, 2018
- Additional Notes: This work was partially supported by JSPS KAKENHI Grants Number 16K05202, 16H03933, 17H02843
- Communicated by: Jeremy Tyson
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 215-227
- MSC (2010): Primary 30C62; Secondary 54H20, 37B35
- DOI: https://doi.org/10.1090/proc/14243
- MathSciNet review: 3876744