Related papers: Variational construction of connecting orbits betw…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…
Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of…
One of the fundamental results of semiclassical theory is the existence of trace formulae showing how spectra of quantum mechanical systems emerge from massive interference among amplitudes related with time-periodic structures of the…
We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing…
We collect some observations about Legendrian links with non-vanishing contact invariants, mostly concerning the non-loose realizations of links and the addition of boundary-parallel half Giroux torsion. In particular, we show that every…
Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated…
Motivated by the ergodic closing lemma of Ma\~n\'e, we investigate the $C^\infty$ closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of periodic orbits generated by $C^\infty$-small…
Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…
This paper considers a class of delay differential equations with unimodal feedback and describes the structure of certain unstable sets of stationary points and periodic orbits. These unstable sets consist of heteroclinic connections from…
The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically problematic. Indeed, it has long been suggested,…
We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: $\bullet$ the integrable part of the hamiltonian may contain a hyperbolic…
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…
We prove gluing theorems for tight contact structures. In particular, we rederive (as special cases) gluing theorems due to Colin and Makar-Limanov, and present an algorithm for determining whether a given contact structure on a handlebody…
We reconsider a control theory for Hamiltonian systems, that was introduced on the basis of KAM theory and applied to a model of magnetic field in previous articles. By a combination of Frequency Analysis and of a rigorous (Computer…
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…