相关论文: A Hopf variables view on the libration points dyna…

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…

We investigate the linear cosmological perturbations in Ho\v{r}ava-Lifshitz gravity with a scalar field. Starting from the most general expressions of the metric perturbations as well as that of a canonical scalar field, we decompose the…

An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…

This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stable focus transitions to an unstable focus by colliding with…

The physics of pions within a finite volume is explored using lattice regularized chiral perturbation theory. This regularization scheme permits a straightforward computational approach to be used in place of analytical continuum…

We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and nonlinear Hamiltonian density. In various…

In this note, we consider generalizations of the asymptotic Hopf invariant, or helicity, for Hamiltonian systems with one-and-a-half degrees of freedom and symplectic diffeomorphisms of a two-disk to itself.

In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…

We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.

The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf-Cole transform of the…

In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…

Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We…

The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…

We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the…

We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…

The Kustaanheimo-Stiefel transformation of the Kepler problem with a time-dependent perturbation converts it into a perturbed isotropic oscillator of 4-and-a-half degrees of freedom with additional constraint known as bilinear invariant.…

We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…

This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…

We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…