Ivar Otto Bendixson

Ivar Otto Bendixson ( born August 1, 1861 in Stockholm, † November 29, 1935 ) was a Swedish mathematician.

Bendixson went to Stockholm to school and studied from 1878 at the Royal Institute of Technology Stockholm and from 1879 at Uppsala University, where in 1881 he received his diploma. He then became a student at the University of Stockholm and was founded in 1880 just after his graduation in 1890 in Uppsala, assistant professor at the University of Stockholm and from 1892 at the Technical University. In 1900 he became a professor of mathematics and in 1905 professor at the University, which he was Rector from 1911 to 1927.

In 1887 he married a banker's daughter.

Work

Bendixson first worked on the set theory by Georg Cantor, in which he is an example of an everywhere non-contiguous perfect amount were, among others, and proved that every non- countable closed set can be decomposed into a perfect set and a countable set ( set of Cantor - Bendixson ).

Today he is known about the behavior of solution curves of ordinary autonomous first order differential equations ( which describe the flow of time dynamic systems in the original investigations Poincaré ) in two dimensions in the vicinity of a singular point, especially for the Poincaré - Bendixson theorem. Either ends the curve in the singular point ( sources, sinks ) or is there a limit cycle (the solution curve encircles the singular point ). Bendixson gave 1901 ( Acta Mathematica Bd.24, Sur les courbes definies par of differential equations. Pp. 1-88 ) his proof independent of Poincaré.

He also studied periodic solutions of differential equations using the method of continued fractions. In the theory of algebraic equations he used Niels Henrik Abel's original method ( without the methods of group theory of Galois ) to explicitly determine the equations whose solutions can be expressed by radicals ( operations root extraction ) ( Abel had fifth in the case of the equation degree shown that this is not always possible).