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On a list of ordinary differential equations problems

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An Editorial Note to this article was published on 28 May 2019

Just as every human undertaking pursues certain objectives, so also mathematical research requires its problems.

It is by the solution of problems that the investigator tests the temper of his steel; he finds new methods and new outlooks, and gains a wider and freer horizon.

D. Hilbert, ICM, Paris. 1900.

Abstract

This evocative essay focuses on the mathematical activities witnessed by the author during 1962–1964 at IMPA. The list of research problems proposed in September 1962 by Mauricio Peixoto at the Seminar on the Qualitative Theory of Differential Equations is pointed out as a landmark for the genesis of the research interest in the Qualitative Theory of Differential Equations and Dynamical Systems in Brazil.

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Notes

  1. Located at the corner of the streets São Clemente and Sorocaba. The two store house hosts now several small shops and a beauty parlor.

  2. This abridged version concerns activities on the QTDE. A wider description can be found in [53].

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Acknowledgements

Thanks are due to Dana Schlomiuk for helpful style suggestions, to Lev Lerman for sending me a copy of [14], to Misha Dokuchaev for helping in its translation and to Maria Lucia Alvarenga for kindly lending the photos in Figs. 2 and 3.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, S.P., 05508-090, Brazil

    Jorge Sotomayor

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  1. Jorge Sotomayor
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Correspondence to Jorge Sotomayor.

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Jorge Sotomayor is fellow of CNPq. Grant: PQ-SR- 307690/2016-4.

This essay contains a very free translation with comments, updates, annotations, additions, corrections and abridgment of “Uma Lista de Problemas de E.D.O.” [53].

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Sotomayor, J. On a list of ordinary differential equations problems. São Paulo J. Math. Sci. 13, 177–194 (2019). https://doi.org/10.1007/s40863-018-0110-3

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