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The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system,…
Thermodynamics provides a unified perspective of thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries,…
We analyse the geodesics' dynamics in cylindrically symmetric vacuum spacetimes with Lambda>0 and compare it to the Lambda=0 and Lambda<0 cases. When Lambda>0 there are two singularities in the metric which brings new qualitative features…
We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…
A general understanding of optimal control in non-equilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear…
It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of…
This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…
In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We introduce a novel concept, called ''sustainability,'' to qualify the long-term evolution of dynamic…
This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…
In a bare site coupled to two reservoirs, we explore the statistics of boson exchange in the presence of two simultaneous processes: squeezing the two reservoirs and driving the two reservoirs. The squeezing parameters compete with the…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is…
Inertia has long been treated as the paradigm of natural motion. This paper challenges this identification through the lens of General Relativity. Drawing on Norton (2012)'s distinction between idealisation and approximation and analysing…
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a…