Related papers: Linearizability of flows by embeddings
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e.\ on compact time sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is…
Flows over time generalize classical network flows by introducing a notion of time. Each arc is equipped with a transit time that specifies how long flow takes to traverse it, while flow rates may vary over time within the given edge…
We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a…
In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Let X be a smooth subvariety of CP^N. We study a flow, called balancing flow, on the space of projectively equivalent embeddings of X, which attempts to deform the given embedding into a balanced one. If L->X is an ample line bundle,…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. When the state space is a solvable connected Lie group, controllability of the linear system is assured if the ad-rank condition holds.
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
We develop mean dimension theory for $\mathbb{R}$-flows. We obtain fundamental properties and examples and prove an embedding theorem: Any real flow $(X,\mathbb{R})$ of mean dimension strictly less than $r$ admits an extension…
In this survey-research paper, we first introduce the theory of Smith classes of complexes with fixed-point free, periodic maps on them. These classes, when defined for the deleted product of a simplicial complex $K$, are the same as the…
A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to design controllers or observers for nonlinear systems. We…
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…
Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.