Coherent sets for nonautonomous dynamical systems

Gary Froyland*, Simon Lloyd, Naratip Santitissadeekorn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Citations (Scopus)


We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications. In this current work, we explain how to extend existing autonomous approaches to the nonautonomous setting. We call the new time-dependent slowly mixing objects coherent sets as they represent regions of phase space that disperse very slowly and remain coherent. The new methods are illustrated via detailed examples in both discrete and continuous time.

Original languageEnglish
Pages (from-to)1527-1541
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Issue number16
Publication statusPublished - 15 Aug 2010
Externally publishedYes


  • Almost-invariant set
  • Coherent set
  • Lyapunov exponent
  • Metastable set
  • Nonautonomous dynamical system
  • Oseledets subspace
  • Perron-Frobenius operator
  • Persistent pattern
  • Strange eigenmode

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