Lucjan Emil Böttcher and his Mathematical Legacy

Domoradzki, Stanisław; Stawiska, Małgorzata

doi:10.1007/978-1-4939-1106-6_5

Cited by 3 publications

(6 citation statements)

References 28 publications

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“…33 Böttcher got his PhD in 1898 in Leipzig under Sophus Lie (1842-1899. He worked on iteration theory and obtained some pioneering results in holomorphic dynamics (Domoradzki, Stawiska 2014). 34 Ernst was a professor of astronomy at Lwów since 1907.…”

Section: Lwówmentioning

confidence: 99%

Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire)

Domoradzki

Stawiska

2018

Stud. Hist. Sci.

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In this article we present diverse experiences of Polish mathematicians (in a broad sense) who during World War I fought for freedom of their homeland or conducted their research and teaching in difficult wartime circumstances. We discuss not only individual fates, but also organizational efforts of many kinds (teaching at the academic level outside traditional institutions, Polish scientific societies, publishing activities) in order to illustrate the formation of modern Polish mathematical community. In Part I we focus on mathematicians affiliated with the existing Polish institutions of higher education: Universities in Lwów in Kraków and the Polytechnical School in Lwów, within the Austro-Hungarian empire.

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Section: Lwówmentioning

confidence: 99%

Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire)

Domoradzki

Stawiska

2018

Stud. Hist. Sci.

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“…He also wrote lecture notes, textbooks for the use in high schools and booklets on spiritualism and afterlife. The (so far most) complete list of his publications can be found in [6].…”

Section: The Life Of Lucjan Emil Böttchermentioning

confidence: 99%

“…He formulated some "fundamental theorems" without proofs, claiming only that they were special cases of some results by Lie. Part II of Böttcher's dissertation was devoted to the study of iterations of rational functions of a complex variable (ranging over the Riemann sphere) and contain results and ideas which can be regarded as foundations of holomorphic dynamics (see further sections or [6] for more information). In part III Böttcher resumed the general study of relations between iteration and functional equations.…”

Section: Böttcher In Leipzigmentioning

confidence: 99%

“…It was only after 1920 that importance of Böttcher's results was realized by other mathematicians (starting with Joseph Fels Ritt, an American who published the first complete proof of Böttcher's theorem). Nowadays Böttcher's theorem is well known to researchers in holomorphic dynamics and functional equations (and was generalized in many ways, see [6]), and he rightly gets the credit for constructing the first example of an everywhere chaotic rational map. But there is more to Lucjan Emil Böttcher's mathematical output that needs to be better known and appreciated.…”

Section: Introductionmentioning

confidence: 99%

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Lucjan Emil Böttcher (1872-1937)-- the Polish pioneer of holomorphic dynamics

Stawiska¹

2013

Preprint

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LUCJAN EMIL B ÖTTCHER (1872-1937)-POLSKI PIONIER DYNAMIKI HOLOMORFICZNEJA b s t r a c t In this article I will present Lucjan Emil Böttcher (1872-1937), a littleknown Polish mathematician active in Lwów. I will outline his scholarly path and describe briefly his mathematical achievements. In view of later developments in holomorphic dynamics, I will argue that, despite some flaws in his work, Böttcher should be regarded not only as a contributor to the area but in fact as one of its founders.

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“…However, by analogy, we call it a "co-dimension 1 Böttcher function. " Those interested in the mathematical legacy of Böttcher should see [10]. We will now briefly describe variants of Böttcher's Theorem in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Superstable manifolds of invariant circles and codimension-one Böttcher functions

Kaschner

Roeder

2013

Ergod. Th. Dynam. Sys.

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Abstract. Let f : X X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of P 1 that is invariant under f , with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose f restricted to this line is given by z → z b , with resulting invariant circle S. We prove that if a ≥ b, then the local stable manifold W s loc (S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition a ≥ b cannot be relaxed without adding additional hypotheses by presenting two examples with a < b for which W s loc (S) is not real analytic in the neighborhood of any point.

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Lucjan Emil Böttcher and his Mathematical Legacy

Cited by 3 publications

References 28 publications

Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire)

Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire)

Lucjan Emil Böttcher (1872-1937)-- the Polish pioneer of holomorphic dynamics

Superstable manifolds of invariant circles and codimension-one Böttcher functions

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