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In $f(T)$ gravity, the theory modifies the gravitational action by introducing a function of the torsion scalar $T$. This approach allows for a different treatment of gravity than general relativity, particularly in cosmological contexts.…
Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
Complex dynamical systems on the Riemann sphere do not possess ``invariant forms''. However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo $\wp$…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
Consider an operator equation (*) $B(u)-f=0$ in a real Hilbert space. Let us call this equation ill-posed if the operator $B'(u)$ is not boundedly invertible, and well-posed otherwise. The DSM (dynamical systems method) for solving equation…
The analytical generalization of the classical dynamical friction formula (derived under the assumption that all the field particles have the same mass) to the case in which the masses of the field particles are distributed with a mass…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
For systems with only short-range forces and shallow 2-body bound states, the typical strength of any 3-body force in all partial-waves, including external currents, is systematically estimated by renormalisation-group arguments in the…
We develop a description of tidal effects in astrophysical systems using effective field theory techniques. While our approach is equally capable of describing objects in the Newtonian regime (e.g. moons, rocky planets, main sequence stars,…