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pro vyhledávání: '"35"'
We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We prove that this notion coincides with the classical Birkhoff attractor. We prove that for the dissipative system associated to the discounted Hamilton-Jacobi equ
Externí odkaz:
http://arxiv.org/abs/2404.00804
Autor:
Masci, Leonardo
We propose a twist condition, inspired by the classical Poincar\'e-Birkhoff theorem on area-preserving maps of the annulus, which applies to asymptotically linear Hamiltonian diffeomorphisms of linear phase space. When an asymptotically linear Hamilt
Externí odkaz:
http://arxiv.org/abs/2403.01855
Autor:
Arathoon, Philip
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of
Externí odkaz:
http://arxiv.org/abs/2310.15035
Autor:
Wagner, Luiz Frederic
In this paper, we first explore holomorphic Hamiltonian systems. In particular, we define action functionals for those systems and show that holomorphic trajectories obey an action principle, i.e., that they can be understood - in some sense - as cri
Externí odkaz:
http://arxiv.org/abs/2303.09480
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity that can be used to give positive topologi
Externí odkaz:
http://arxiv.org/abs/2208.13041
Autor:
Wang, Hong
In order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a good expr
Externí odkaz:
http://arxiv.org/abs/2110.14175
Autor:
Chaidez, Julian, Edtmair, Oliver
Let $X \subset \mathbb{R}^4$ be a convex domain with smooth boundary $Y$. We use a relation between the extrinsic curvature of $Y$ and the Ruelle invariant $\text{Ru}(Y)$ of the natural Reeb flow on $Y$ to prove that there exist constants $C > c > 0$
Externí odkaz:
http://arxiv.org/abs/2012.12869
Autor:
Alonso, Jaume, Hohloch, Sonja
Publikováno v:
Journal of Nonlinear Science, 31, 51 (2021)
Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vu Ngoc about a decade ago in terms of five symplectic invariants. If a semitoric system has sev
Externí odkaz:
http://arxiv.org/abs/2006.15369
Publikováno v:
Trans. Amer. Math. Soc. 374 (2021), 1815-1845
We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by sh
Externí odkaz:
http://arxiv.org/abs/1808.06995
Autor:
Gong, Wenmin
In this paper we establish the existence of periodic orbits belonging to any $\sigma$-atoroidal free homotopy class for Hamiltonian systems in the twisted disc bundle, provided that the compactly supported time-dependent Hamiltonian function is suffi
Externí odkaz:
http://arxiv.org/abs/1801.08773