|Lucjan Emil Böttcher|
|Alma mater||Lwów Polytechnic School, University of Leipzig|
|Known for||Böttcher's equation|
|Thesis||Beiträge zu der Theorie der Iterationsrechnung (1898)|
|Doctoral advisor||Sophus Lie|
Böttcher was born on January 21, 1872, in Warsaw, Poland. He attended private schools in Warsaw and graduated from the classical gymnasium in Łomża in 1893, after which he entered the Imperial University of Warsaw in the Division of Mathematics and Physics. At the time, Russian was the language of instruction at the university, as Warsaw was under Russian rule.
He was expelled from the university for participation in patriotic (anti-Russian) demonstrations in 1894. He moved to Lwów Polytechnic School, where he obtained a so-called half-diploma in 1897. Desiring to continue his mathematical education, he moved to Leipzig, where he worked under Sophus Lie. His doctoral thesis, published in 1898, was titled Beiträge zu der Theorie der Iterationsrechnung.
Böttcher married Maria Wolle in 1900, and had four children.
Following his doctorate, Böttcher returned to Lwów to take up a junior position at the Lwów Polytechnic School. By 1911, he was licensed to teach (venia legendi) at the school, and he offered courses on theoretical mechanics as well as mathematics for engineering. All his attempts to obtain habilitation at the University of Lwów failed, however. This meant that he was not permitted to guide doctoral students.
Böttcher was a member of the Polish Mathematical Society. He took seriously his role of an educator, encouraging the introduction of differential and integral calculus at school level, and writing several high-school textbooks. One example is Principles of Elementary Algebra, adapted to the curriculum in the Polish Kingdom (1911), which followed the so-called Meran programme that aimed to teach students to think in terms of functions.
Böttcher's most important work was in the iterations of rational mappings of the Riemann sphere. His name is attached to Böttcher theorem, in which he introduced Böttcher's equation and solved it under certain assumptions. He obtained results about the orbits of iterated rational maps, studied their convergence regions (Fatou components) and boundaries (Julia set); he also gave examples of everywhere chaotic maps constructed via elliptic functions. Indeed, his example of rational maps whose chaotic set is the entire sphere predated the more famous Lattès examples by over twenty years.
Böttcher was one of the founders of Holomorphic dynamics, which he viewed as a part of the mathematical theory of iterational calculus. Despite his achievements, however, his early publications were considered insufficient to warrant a habilitation at the University of Lwow in 1901. Seventeen years later, with more publications to his name, he approached the University again for habilitation, but his request was denied. The committee's criticism focused on erroneous and unscientific reasoning in some of his papers, and cited the lack of clarity even in his expository works.
As Böttcher worked in a mathematical discipline considerably removed from the interests of other Lwów mathematicians, he found little support from his peers. Indeed, his partial results and conclusions were forgotten, and a complete theory came about only decades later following the independent investigations of Pierre Fatou, Gaston Julia, Samuel Lattès and Salvatore Pincherle.
Böttcher retired from the Polytechnic School in 1935. He died in Lwów on May 29, 1937.
- Beiträge zu der Theorie der Iterationsrechnung (Ph.D.). Oswald Schmidt. 1898.
- "Zasady rachunku iteracyjnego (część pierwsza, część druga)". Prace Matematyczno Fizyczne. X: 65–86, 86–101. 1899–1900.
- "Zasady rachunku iteracyjnego (część III)". Prace Matematyczno Fizyczne. XII: 95–111. 1901.
- "Zasady rachunku iteracyjnego (część III, dokończenie)". Prace Matematyczno Fizyczne. XIII: 353–371. 1902.
- "Glavnyshiye zakony skhodimosti iteratsiy i ikh prilozheniya k' analizu". Bulletin de la Societe Physico-Mathematique de Kasan. XIII (1): 137. 1903.
- "Glavnyshiye zakony skhodimosti iteratsiy i ikh prilozheniya k' analizu". Bulletin de la Societe Physico-Mathematique de Kasan. XIV (2): 155–200. 1904.
- "Glavnyshiye zakony skhodimosti iteratsiy i ikh prilozheniya k' analizu". Bulletin de la Societe Physico-Mathematique de Kasan. XIV (3): 201–234. 1904.
- Principles of geometry with numerous exercises. Warsaw: M. Arct. 1908.
- Principles of Elementary Algebra, adapted to the curriculum in the Polish Kingdom. Warsaw. 1911.
- Domoradzki, Stanisław; Stawiska, Małgorzata (July 11, 2012). "Lucjan Emil Böttcher and his mathematical legacy". arXiv: .
- Stawiska, Małgorzata (November 15, 2013). "Lucjan Emil Böttcher (1872–1937) - The Polish Pioneer of Holomorphic Dynamics". arXiv: .
- Eremenko, A.E.; Lyubich, M.Yu. (1990). "The dynamics of analytic transformations". Leningrad Math. J. 1 (3): 563–634.
- Alexander, Daniel S. (1994), A history of complex dynamics. From Schröder to Fatou and Julia, Aspects of Mathematics, E24, Braunschweig: Friedr. Vieweg & Sohn
- Alexander, Daniel S.; Iavernaro, Felice; Rosa, Alessandro (2012), Early days in complex dynamics. A history of complex dynamics in one variable during 1906-1942, History of Mathematics, 38, American Mathematical Society, Providence, RI; London Mathematical Society, London
- Domoradzki, Stanisław (2010), "Mathematics in Lwów before the Lwów Mathematical School,", in Martina Bečvářová and Christa Binder, Mathematics in the Austrian-Hungarian Empire: Proceedings of a Symposium held in Budapest on August 1, 2009 during the XXIII ICHST, Praha: Matfyzpress, pp. 55–73, ISBN 978-80-7378-114-9
- Domoradzki, Stanisław (2011), The Growth of Mathematical Culture in the Lvov Area in the Autonomy Period (1870-1920), History of Mathematics, 47, Praha: Matfyzpress