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We establish the dynamical attractor behavior in scalar-tensor theories of dark energy, providing a powerful framework to analyze classes of theories, predicting common evolutionary characteristics that can be compared against cosmological…
It is shown that the distributed chaos in the simple Hamiltonian (conservative) dynamical systems, such as the Nose-Hoover oscillator and double oscillator, can mimic the distributed chaos in the isotropic homogeneous turbulence. Direct…
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that…
We use the Jordan frame-Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe describes the late-time…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and…
We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe…
The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…
Dynamic behaviour of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analysed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help…
We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all…
We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Dynamics of an anisotropic universe is studied in $f(R,T)$ gravity using a rescaled functional $f(R,T)$. Three models have been constructed assuming a power law expansion of the universe. Physical features of the models are discussed. The…
The fundamentals of Brownian motion have been largely well understood since the early 20th century, with most recent additions focusing on understanding anomalous diffusion via rescaling of drag coefficents. That focus emphasizes long-time…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The dynamics of any spherical cosmology with a scalar field (`scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the `time' parameter. The…
In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a…