Related papers: A parametrization algorithm to compute lower dimen…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obtained through the $\Omega$-modified procedure is equivalent…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
We present a method of localised control of chaos in Hamiltonian systems. The aim is to modify the perturbation locally by a small control term which makes the controlled Hamiltonian more regular. We provide an explicit expression for the…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
By applying the Hamiltonian reduction scheme we recover the R-matrix of the trigonometric and elliptic Calogero-Moser system.
We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial guesses. No preferred coordinate system is required, meaning…
This paper investigates the effect of random perturbations, in particular multiplicative noise, on the integrable structure of Hamiltonian systems, with a particular focus on KAM theory for stochastic Hamiltonian dynamics. We prove that,…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…
We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based…
It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…
The paper aims at constructing two different solutions to an elliptic system $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers…
For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…
Recently Hirota and Kimura presented a new discretization of the Euler top with several remarkable properties. In particular this discretization shares with the original continuous system the feature that it is an algebraically completely…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
This survey gives a short and comprehensive introduction to a class of finite-dimensional integrable systems known as hypersemitoric systems, recently introduced by Hohloch and Palmer in connection with the solution of the problem how to…