  "Phase-locking" is a fundamental phenomenon in which coupled or periodically
forced oscillators synchronise. The Arnold family of circle maps, which
describes a forced oscillator, is the simplest mathematical model of
phase-locking and has been studied intensively since its introduction in the
1960s. The family exhibits regions of parameter space where phase-locking
phenomena can be observed. A long-standing question asked whether "hyperbolic"
parameters~-- those whose behaviour is dominated by periodic attractors, and
which are therefore stable under perturbation~-- are dense within the family. A
positive answer was given in 2015 by van Strien and the author, which implies
that, no matter how chaotic a map within the family may behave, there are
always systems with stable behaviour nearby. This research was a focal point of
a pioneering collaboration with composer Emily Howard, commencing with Howard's
residency in Liverpool's mathematics department in 2015. The collaboration
generated impacts on creativity, culture and society, including several musical
works by Howard, and lasting influence on artistic practice through a
first-of-its-kind centre for science and music. We describe the research and
the collaboration, and reflect on the factors that contributed to the latter's
success.
