TL;DR
This paper introduces a method to construct simple completely integrable systems around singular levels with non-degenerate singularities, using the cotangent bundle of the desingularized level to realize the associated affine structure.
Contribution
It presents a novel construction technique for integrable systems based on the affine structure of singular levels, with applications to various types of non-degenerate singularities.
Findings
Constructed integrable systems with prescribed singular affine structures
Provided examples of systems with different non-degenerate singularities
Demonstrated the use of cotangent bundles in system construction
Abstract
Any singular level of a completely integrable system (c.i.s.) with non-degenerate singularities has a singular affine structure. We shall show how to construct a simple c.i.s. around the level, having the above affine structure. The cotangent budle of the desingularised level is used to perform the construction, and the c.i.s. obtained looks like the simplest one associated to the affine structure. This method of construction is used to provide several examples of c.i.s. with different kinds of non-degenerate singularities.
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Taxonomy
TopicsElasticity and Wave Propagation