相关论文: Koopman operators and the $3x+1$-dynamical system

Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear…

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this…

Methods for constructing causal linear models from nonlinear dynamical systems through lifting linearization underpinned by Koopman operator and physical system modeling theory are presented. Outputs of a nonlinear control system, called…

The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…

By introducing the busy beaver competition of Turing machines, in 1962, Rado defined noncomputable functions on positive integers. The study of these functions and variants leads to many mathematical challenges. This article takes up the…

A suite of three evolution systems is presented in the framework of the 3+1 formalism. The first one is of second order in space derivatives and has the same causal structure of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system for a…

Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising…

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…

A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex…

We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…

Take an odd number x >0. Then 3x+1 is even and one can find an integer k> 0 so that y= 3x+1/2^k is again odd. We get in this way the mapping T, Tx=y. The paper contains two theorems describing statistical properties of T. The first…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…

This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an…

This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…

We present a finite-state, deterministic automaton that emulates the Collatz function through digitwise transitions on base-10 representations. Each digit is represented as a symbolic triplet (r, p, c) encoding its value, the parity of the…

Despite impressive dexterous manipulation capabilities enabled by learning-based approaches, we are yet to witness widespread adoption beyond well-resourced laboratories. This is likely due to practical limitations, such as significant…