Oscillations de systèmes hamiltoniens non linéaires. III
Oscillations forcées de systèmes hamiltoniens non linéaires
Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange
Oscillatory Solutions in the Planar Restricted Three-Body Problem.
Overview of the differential Galois integrability conditions for non-homogeneous potentials
We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form , where and are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable...
Parabolic perturbations of Hamilton–Jacobi equations
We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
Parameter influence on passive dynamic walking of a robot with flat feet
The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...
Particle Dynamics Modelling of Cell Populations
Evolution of cell populations can be described with dissipative particle dynamics, where each cell moves according to the balance of forces acting on it, or with partial differential equations, where cell population is considered as a continuous medium. We compare these two approaches for some model examples
Particles in the superworldline and BRST
In this short note we discuss -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- fields are in the first BRST cohomology group. For , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.
Particles, phases, fields
The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...
Pattern Formation of Competing Microorganisms in Sediments
We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature. We...
Periodic derivative of solutions to nonlinear differential equations
Periodic orbits close to elliptic tori and applications to the three-body problem
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses...
Periodic points and chaotic-like dynamics of planar maps associated to nonlinear Hill's equations with indefinite weight.
Periodic solutions for a class of autonomous hamiltonian systems
Periodic solutions for N-body type problems
Periodic solutions for second order Hamiltonian systems
By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.
Periodic solutions for second-order Hamiltonian systems with a p -Laplacian
In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
Periodic solutions of a non coercive Hamiltonian system.
Periodic Solutions of Asymptotically Linear Hamiltonian Systems.