## Ergodic Theory, Open Dynamics, and Coherent StructuresWael Bahsoun, Christopher Bose, Gary Froyland This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior. |

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### Contents

1 | |

2 Eigenvalues of Transfer Operators for Dynamical Systems with Holes | 31 |

3 Periodic Points Escape Rates and Escape Measures | 41 |

4 A Multitime Step Method to Compute Optical Flowwith Scientific Priors for Observations of a Fluidic System | 59 |

5 Numerical Approximation of Conditionally Invariant Measures via Maximum Entropy | 80 |

6 Lebesgue Ergodicity of a Dissipative Subtractive Algorithm | 105 |

7 Improved Estimates of Survival Probabilities via Isospectral Transformations | 119 |

8 Dispersing Billiards with Small Holes | 136 |

Directionality Duration and Diffusion | 171 |

10 ReturnTime Statistics HittingTime Statistics and Inducing | 217 |

### Other editions - View all

Ergodic Theory, Open Dynamics, and Coherent Structures Wael Bahsoun,Christopher Bose,Gary Froyland No preview available - 2014 |

Ergodic Theory, Open Dynamics, and Coherent Structures Wael Bahsoun,Christopher Bose,Gary Froyland No preview available - 2014 |

Ergodic Theory, Open Dynamics, and Coherent Structures Wael Bahsoun,Christopher Bose,Gary Froyland No preview available - 2016 |

### Common terms and phrases

ACCIMs advective Algorithm almost-invariant sets approximation autonomous billiard boundary bounded components compute conditionally invariant measures consider convergence corner points corresponding data term defined denote density dynamical systems eigenvalue eigenvector Ergodic Theory escape rate estimate exponential f.Nx finite finite-time coherent sets fixed fluid flux follows Froyland FTLE heteroclinic hyperbolic intersection interval Œ0 invariant measures iterate Lagrangian coherent structures Lebesgue measure Lemma lobe Lyapunov exponents Markov Markov partition Math Mathematics matrix Melnikov function nonautonomous Nonlinearity numerical obtained open dynamical system open system optical flow optimal orbits partition Perron-Frobenius operator perturbed phase space Phys probability measure problem Proof properties Proposition regularization terms respect satisfies Sect self-adjoint operator sequence singular vector spectral Springer Springer Science+Business Media stable and unstable stable curves Statistics stream function Subcase Theorem time-dependent trajectories transfer operator transport two-dimensional unstable manifolds vector fields zero