Zobrazeno 1 - 10
of 534
pro vyhledávání: '"MCLACHLAN, ROBERT I."'
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of this pape
Externí odkaz:
http://arxiv.org/abs/2402.05393
Publikováno v:
Journal of Computational Dynamics, 2024
We show that any Lotka--Volterra tree-system associated with an $n$-vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also prove that the Kahan discretisation of these tree-systems factorises
Externí odkaz:
http://arxiv.org/abs/2309.05979
Autor:
McLachlan, Robert I
We study two existing extended phase space integrators for Hamiltonian systems, the {\em midpoint projection method} and the {\em symmetric projection method}, showing that the first is a pseudosymplectic and pseudosymmetric Runge--Kutta method and t
Externí odkaz:
http://arxiv.org/abs/2308.06516
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a chaotic attrac
Externí odkaz:
http://arxiv.org/abs/2307.05144
The main result of this paper is the discretization of Hamiltonian systems of the form $\ddot x = -K \nabla W(x)$, where $K$ is a constant symmetric matrix and $W\colon\mathbb{R}^n\to \mathbb{R}$ is a polynomial of degree $d\le 4$ in any number of va
Externí odkaz:
http://arxiv.org/abs/2303.04300
Publikováno v:
Forum of Mathematics Sigma 11 (2023), E69
Aromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-preserving B-series method is the exact flow of the differential equation.
Externí odkaz:
http://arxiv.org/abs/2301.10998
Autor:
McLachlan, Robert I, Offen, Christian
Publikováno v:
Journal of Geometric Mechanics, volume 15, issue 1, pages 98-115, 2023
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analy
Externí odkaz:
http://arxiv.org/abs/2201.03911
Autor:
McLachlan, Robert I., Stern, Ari
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important properties o
Externí odkaz:
http://arxiv.org/abs/2111.10042
Publikováno v:
ANZIAM J. 59 (MINZ2017) pp. M63-M125, 2022
The New Zealand National Policy Statement for Freshwater Management 2020 sets several targets for freshwater quality, six of which are measurements of rivers; others relate to lakes. Each regional council is required to monitor freshwater quality and
Externí odkaz:
http://arxiv.org/abs/2110.01808
Global resonance is a mechanism by which a homoclinic tangency of a smooth map can have infinitely many asymptotically stable, single-round periodic solutions. To understand the bifurcation structure one would expect to see near such a tangency, in t
Externí odkaz:
http://arxiv.org/abs/2108.07476