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of 750
pro vyhledávání: '"70H06"'
The vanishing of the Haantjes tensor is an important property that has been linked, for instance, to the existence of separation coordinates and the integrability of systems of hydrodynamic type. We discuss the vanishing of the Haantjes tensor for op
Externí odkaz:
http://arxiv.org/abs/2412.13007
Autor:
Agapov, Sergei
We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn o
Externí odkaz:
http://arxiv.org/abs/2411.18920
Hypersemitoric systems are a class of integrable systems on $4$-dimensional symplectic manifolds which only have mildly degenerate singularities and where one of the integrals induces an effective Hamiltonian $S^1$-action and is proper. We introduce
Externí odkaz:
http://arxiv.org/abs/2411.17509
Autor:
Hohloch, Sonja, Santos, Pedro
We adapt and generalize McDuff's method of probes from toric system to so called semitoric integrable systems and apply it to study the (non)displaceability properties of the fibers of $3$ examples of semitoric integrable systems.
Comment: 48 pa
Comment: 48 pa
Externí odkaz:
http://arxiv.org/abs/2411.16601
Autor:
Nugent, Jeremy, Vollmer, Andreas
We obtain a necessary and sufficient condition for a second-order superintegrable systems with $(n+1)$-parameter potential to arise from a non-degenerate system via the restriction of the non-degenerate potential.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2411.06994
We present two involutivity theorems in the context of Poisson quasi-Nijenhuis manifolds. The second one stems from recursion relations that generalize the so called Lenard-Magri relations on a bi-Hamiltonian manifold. We apply these results to the c
Externí odkaz:
http://arxiv.org/abs/2410.08671
Autor:
Armstrong, John, Vollmer, Andreas
We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant superintegrable s
Externí odkaz:
http://arxiv.org/abs/2410.05009
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geometry. This text has grown out from preparatory materials for the series
Externí odkaz:
http://arxiv.org/abs/2410.04276
Autor:
Henriksen, Tobias Våge
We show that su(2) rational and trigonometric Gaudin models, or in other words, generalised coupled angular momenta systems, have singularities that undergo Hamiltonian Hopf bifurcations. In particular, we find a normal form for the Hamiltonian Hopf
Externí odkaz:
http://arxiv.org/abs/2410.01372
The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg--de Vries, coupled KdV, Harry Dym, coup
Externí odkaz:
http://arxiv.org/abs/2410.00895