Related papers: Generalized modified gravity models: the stability…
Spatially homogeneous cosmological models with a positive cosmological constant are investigated, using dynamical systems methods. We focus on the future evolution of these models. In particular, we address the question whether there are…
We study the evolution of cosmological perturbations in f(G) gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term G. We derive the equations for perturbations assuming…
We examine some kinds of discrete symmetries which are dynamically preserved, using the (generalized) Gowdy models of the first kind.
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to…
We investigate the dynamics of the chameleonic Generalised Brans--Dicke model in flat FRW cosmology. In a new approach, a framework to study stability and attractor solutions in the phase space is developed for the model by simultaneously…
We obtain conditions for the existence and stability of de Sitter attractors in the phase space of spatially homogeneous and isotropic cosmology in generalized theories of gravity (including non-linear and scalar-tensor theories). These…
In this paper we study cosmological solutions of the $f(T,B)$ gravity using dynamical system analyses. For this purpose we consider cosmological viable functions of $f(T,B)$ that are capable of reproducing the dynamics of the Universe. We…
We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
We use asymptotic methods to study the early time stability of isotropic and homogeneous solutions filled with radiation which are close initially to the exact, flat, radiation solution in quadratic lagrangian theories of gravity. For such…
We explore some cosmological features of the newly suggested 4D Gauss-Bonnet gravity through two different models assuming a varying cosmological constant. Observational constraints, such as the cosmic transit and the flat curvature, have…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated…
We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates…
In this work, we study cosmological spacetime configurations in $f(Q)$ gravity with nonvanishing symmetric teleparallel connections. It is known that the spatially flat, homogeneous and isotropic connections can be classified into three…