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Open problems, questions and challenges in finite- dimensional integrable systems.

Alexey Bolsinov^1,2, Vladimir S Matveev³, Eva Miranda^4,5

¹Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK A.Bolsinov@lboro.ac.uk.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|September 19, 2018

Summary

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This summary is machine-generated.

This paper explores open problems in finite-dimensional integrable systems, drawing from a 2017 conference. It highlights current research trends and future questions in the field.

Area of Science:

Mathematical Physics
Dynamical Systems

Background:

Integrable systems with finitely many degrees of freedom are a key area in mathematical physics.
Recent advancements necessitate a review of outstanding challenges and future research directions.

Purpose of the Study:

To survey open problems and questions in finite-dimensional integrable systems.
To consolidate insights from the 'Finite-dimensional Integrable Systems, FDIS 2017' conference.

Main Methods:

Literature review and synthesis of expert contributions.
Compilation of research questions posed by conference participants.

Main Results:

Identified and categorized numerous open problems across various aspects of the field.

Keywords:

Lagrangian fibration Poisson manifold integrable system

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Provided a snapshot of the state-of-the-art and emerging trends in integrable systems research.

Conclusions:

The survey serves as a valuable resource for researchers in integrable systems.
It outlines critical areas for future investigation and collaboration.