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pro vyhledávání: '"37j35"'
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
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In this paper,
Externí odkaz:
http://arxiv.org/abs/2411.16631
One way to define a sub-Riemannian metric is as the limit of a Riemannian metric. Consider a Riemannian structure depending on a parameter $s$ such that its limit defines a sub-Riemannian metric when $s \to \infty$, assuming that the Riemannian geode
Externí odkaz:
http://arxiv.org/abs/2411.09008
Autor:
Vollmer, Andreas
We show that two natural and a priori unrelated structures encapsulate the same data, namely certain commutative and associative product structures and a class of superintegrable Hamiltonian systems. More precisely, consider a Euclidean space of dime
Externí odkaz:
http://arxiv.org/abs/2411.06418
In this paper we propose a geometric approach to study Painlev\'e equations appearing as constrained systems of three first-order ordinary differential equations. We illustrate this approach on a system of three first-order differential equations ari
Externí odkaz:
http://arxiv.org/abs/2411.01657
Autor:
Vollmer, Andreas
Second-order (maximally) conformally superintegrable Hamiltonian systems of abundant type are re-examined, revealing their underlying Weylian geometry. This allows one to naturally extend the concept of c-superintegrability from the realm of conforma
Externí odkaz:
http://arxiv.org/abs/2411.00569
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
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