相关论文: Equilibrium sets in quintom cosmologies: the past …
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We…
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a…
A new kind of evolution for cyclic models in which the Hubble parameter oscillates and keeps positive has been explored in a specific $f(R,T)$ gravity reconstruction. A singularity-free cyclic universe with negative varying cosmological…
This paper is concerned with parabolic gradient systems of the form \[ u_t=-\nabla V (u) + u_{xx}\,, \] where the spatial domain is the whole real line, the state variable $u$ is multidimensional, and the potential $V$ is coercive at…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
We investigate the long-term dynamics of a five-dimensional nonlinear system describing the non-ideal excitation of a spherical pendulum coupled to a limited-power electric motor. By analyzing the phase trajectories y(t) = (y1, y2, y3, y4,…
In this paper, the dynamical heteroclinic orbit and attractor have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviates the fine tuning problem in cosmological dynamical system…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power…
In this work, a global dynamical analysis of spatially flat FLRW cosmologies driven by a canonical scalar field minimally coupled to gravity is presented. Under suitable regularity and asymptotic assumptions on the scalar field potential,…
We present a comprehensive phase-space analysis of a quadratic dark energy model where the pressure includes a nonlinear term proportional to the square of the energy density. This minimal extension beyond the $\Lambda$CDM framework…
We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…
We investigate the features of the cosmological expansion history described by a recent model of gravity characterised by two nonlocally interacting metrics. We perform a detailed analysis of the dynamical system formed by the field…
The magnitudes of the terms in periodic orbit semiclassical trace formulas are determined by the orbits' stability exponents. In this paper, we demonstrate a simple asymptotic relationship between those stability exponents and the…
In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the…
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of…