Related papers: Time-Dependent 2-D Vector Field Topology: An Appro…
Recall that a vector field on an n-dimensional differentiable manifold M is a mapping X defined on M with values in the tangent bundle TM that assigns to each point $x\in M$ a vector X(x) in the tangent space $T_x M$. A vector field may be…
This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis and the global, operator theoretic, Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov…
Given a finite set of data generated by an unknown ordinary differential equation it is impossible to exactly determine the associated vector field, and hence, bifurcation theory tells us that it is impossible, in general, to correctly…
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…
The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related…
Time series prediction is crucial for understanding and forecasting complex dynamics in various domains, ranging from finance and economics to climate and healthcare. Based on Transformer architecture, one approach involves encoding…
We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
This paper gives a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.
We show an example providing a significance in geometric control theory of the existence of the dependence locus of a system of vector fields in particular, the generic appearance of non-trivial singular trajectories embedded in the…
In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…
Biadjoint scalar field theories appear in the study of scattering amplitudes and classical solutions in gauge, gravity and related theories. In this paper, we present new exact solutions of biadjoint scalar field theory, showing that…
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a…
Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy…
We discuss topological Landau-Ginzburg theories coupled to the 2-dimensional topological gravity. We point out that the basic recursion relations for correlation functions of the 2-dimesional gravity have exactly the same form as the…
In analogy to valued fields, we study model-theoretic properties of valued vector spaces with variable base field by proving transfer principles down to the skeleton and down to the value set and base field. For instance, we give a formula…
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…
Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…