Publication details.

Paper

Year:	2016
Author(s):	J.H.E. Cartwright, N. Piro, O. Piro, I. Tuval
Title:	Geometric phases in discrete dynamical systems
Journal:	PHYSICS LETTERS A
ISSN:	0375-9601
JCR Impact Factor:	1.772
Volume:	380
Issue No.:	42
Pages:	3485-3489
D.O.I.:	10.1016/j.physleta.2016.08.050
Web:	http://www.sciencedirect.com/science/article/pii/S0375960116306594
Abstract:	In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.