128 citations · 592 across the 51 of their papers we have counts for
4 papers · 1 filter
Runge--Kutta methods determined from extended phase space methods for Hamiltonian systems
Robert I McLachlan
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 fir…
Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps
Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson
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 applic…
Birational maps from polarization and the preservation of measure and integrals
Robert I McLachlan, David I McLaren, G R W Quispel
The main result of this paper is the discretization of Hamiltonian systems of the form , where is a constant symmetric matrix and $W\colon\mathbb{R}^n…
The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators
Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas +1
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-pres…