Related papers: Andoyer construction for Hill and Delaunay variabl…

Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…

We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R->{0,1} functions.

Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…

Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…

A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…

We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try…

Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a successful approach. However, when the solution depends on elliptic functions the transformation to action-angle variables may need to remain in…

We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…

Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods are, however, either parametric or cease to perform well when the data is far from linearly…

Statistical prediction models are often trained on data from different probability distributions than their eventual use cases. One approach to proactively prepare for these shifts harnesses the intuition that causal mechanisms should…

Loewner hulls are determined by their real-valued driving functions. We study the geometric effect on the Loewner hulls when the driving function is composed with a random time change, such as the inverse of an $\alpha$-stable subordinator.…

We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

We suggest that proper variables for the description of non-Abelian theories are those gauge invariant ones which keep the invariance of the winding number functional with respect to topologically nontrivial (large) gauge transformations.…

This paper presents a simple, one-dimensional model of a randomly advected passive scalar. The model exhibits anomalous inertial range scaling for the structure functions constructed from scalar differences. The model provides a simple…

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…

In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…