title: General approach for dealing with dynamical systems with spatiotemporal periodicities.
abstract: Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc. In particular, we are able to show that simple symmetry considerations determine, to a large extent, how their properties depend functionally on some of the parameters of the periodic terms. For the sake of illustration, we apply this formalism to find the functional dependence of the expectation value of the momentum of a Bose-Einstein condensate, described by the Gross-Pitaewskii equation, when it is exposed to a sawtooth potential whose amplitude is periodically modulated in time. We show that, by using this formalism, a small set of measurements is enough to obtain the functional form for a wide range of parameters. This can be very helpful when characterizing experimentally the response of systems for which performing measurements is costly or difficult.
authors.affiliation: Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain.
authors.forename: Jesús
authors.initials: J
authors.lastname: Casado-Pascual
authors.affiliation: Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza, Spain.
authors.forename: José A
authors.initials: JA
authors.lastname: Cuesta
authors.affiliation: Instituto de Matemáticas de la Univesidad de Sevilla (IMUS).|Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain.
authors.forename: Niurka R
authors.initials: NR
authors.lastname: Quintero
authors.affiliation: Instituto de Matemáticas de la Univesidad de Sevilla (IMUS).|Departamento de Análisis Matemático, Universidad de Sevilla, Apdo 1160, 41080 Sevilla, Spain.
authors.forename: Renato
authors.initials: R
authors.lastname: Alvarez-Nodarse