title: OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
abstract: Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝNusing a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated withC1maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-Tmaps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
authors.affiliation: Department of Mathematics, University of Houston, URL : http://www.math.uh.edu/~ott/.
authors.forename: William
authors.initials: W
authors.lastname: Ott
authors.affiliation: Department of Mathematics, Wake Forest University.
authors.forename: Mauricio A
authors.initials: MA
authors.lastname: Rivas
authors.affiliation: Department of Mathematics, University of Houston, URL : http://www.math.uh.edu/~jdwest/.
authors.forename: James
authors.initials: J
authors.lastname: West
keywords: Embedding; Lyapunov exponent; induced dynamics; infinite-dimensional dynamical system; prevalence