… which are defined as ridges of Finite-Time Lyapunov Exponent (FTLE) fields. These ridges
can … applicable to flows with arbitrary time dependence and, in particular, to flows that are only …

… Lyapunov exponents for almost all initial conditions ensures nonperiodic behavior of chaotic
flows… In the present paper we summarize basic properties of Lyapunov exponents, and …

… defined, as are all negative Lyapunov exponents > κ. As will … zero Lyapunov exponent,
namely the exponent in “the flow … : either (1) μ is supported on a periodic orbit, or (2) there are …

… Aperiodic behaviour of physical systems, which has been encountered so often, is now being
analyzed … Because the Lyapunov exponents are a dynamical invariant, we can use the flow …

… Here, we propose a simple way to extend the phase flow method to aperiodic flows. For …
To apply the backward phase flow method to an aperiodic flow, we convert the flow field into …

… A transition to aperiodic flow was observed at R/R, = 11.7. Extensive tests of the aperiodic
state at and past transition showed that the flow exhibited lowdimensional chaos. Henceforth, …

… (the finite-time Lyapunov exponent is simply the logarithm of … of finite-time Lyapunov
exponents and computed results for … of finite-time Lyapunov exponents for atmospheric flow in the …

… A periodic flow is an idealization of an homogeneous flow, and leads to the minimum
computational constraint. The maximum resolution that we shall consider is 1B2 in two-…

… finite-time Lyapunov exponent (FTLE) fields in unsteady flows. The methods approximate
the particle flow map, eliminating redundant particle integrations in neighboring flow map …

… and flows, uniqueness and the ergodic properties of equilibrium states and so on ([2], [3], [7]). …
To prove the theorem we shall show how to find a periodic point in the ball B(^o, s) for a …