Manuscript Topics

Lie groups and algebras have become an essential tool in many geometrical and analytical problems, constituting a powerful source of techniques that provide effective procedures to understand the evolution of several types of physical phenomena and their interactions. Modern developments in Differential Geometry and Operator Theory have provided additional tools and perspectives that offer new possibilities, opening new research fields and applications in Geometric Mechanics. The Lie Symmetry method, Lie systems and their generalizations, such as Lie—Hamilton, Dirac—Lie, Jacobi—Lie or k-Symplectic Lie systems have been to be deeply connected with fundamental notions like conservation laws and space-time geometry, as well as to (Liouville) integrability and super-integrability of dynamical systems.

We invite researchers to contribute original papers as well as review articles that stimulate the continuing efforts towards a unified comprehension of Lie groups in the context of Geometric Mechanics and their implication in adjacent disciplines. We are particularly interested in articles describing new methods and applications of Lie group theoretic methods and representation theory in the context of Geometric Mechanics. More general or alternative structures are also welcome, including current developments in the application of these techniques.

The aim of this Issue is to publish original research articles covering (but not limited to) any of the following topics:  
• Calculus of Variations and Lie Groups in Geometric Mechanics  
• Computational Lie Theory in Geometric Mechanics  
• Hidden symmetries and non-locality  
• Higher algebraic structures and (super)-integrability  
• (Generalized) symmetries of mechanical systems  
• Applications to non-linear realisations of Lie algebras and invariant theory  
• New classification methods

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