The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference 'Finite-dimensional Integrable Systems, FDIS 2017' held at CRM, Barcelona in July 2017.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.
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Bolsinov et al. (2018) studied this question.
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