| Description |
1 online resource (xvi, 227 pages) : illustrations (some color) |
| Series |
Springer proceedings in mathematics & statistics, 2194-1009 ; volume 70 |
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Springer proceedings in mathematics & statistics ; v. 70.
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| Contents |
880-01 1. Nonautonomous flows as open dynamical systems: characterising escape rates and time-varying boundaries -- 2. Eigenvalues of transfer operators for dynamical systems with holes -- 3. Periodic points, escape rates and escape measures -- 4. A multi-time step method to compute optical flow with scientific priors for observations of a fluidic system -- 5. Numerical approximation of conditionally invariant measures via maximum entropy -- 6. Lebesgue ergodicity of a dissipative subtractive algorithm -- 7. Improved estimates of survival probabilities via isospectral transformations -- 8. Dispersing billiards with small holes -- 9. Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion -- Return-time statistics, hitting-time statistics, and inducing |
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880-01/(S Machine generated contents note: 1.1. Introduction / Sanjeeva Balasuriya -- 1.2. Perturbative Setting / Sanjeeva Balasuriya -- 1.3. Boundaries Between Open Dynamical Systems: Invariant Manifolds / Sanjeeva Balasuriya -- 1.4. Flux Quantification / Sanjeeva Balasuriya -- 1.5. Simplifications of Flux Formula in the Subcases / Sanjeeva Balasuriya -- 1.6. Concluding Remarks / Sanjeeva Balasuriya -- References / Sanjeeva Balasuriya -- 2.1. Introduction / Oscar F. Bandtlow / Oliver Jenkinson -- 2.2. Eigenvalue Estimates via Weyl's Inequality / Oscar F. Bandtlow / Oliver Jenkinson -- 2.3. Common Spectrum / Oscar F. Bandtlow / Oliver Jenkinson -- 2.4. Hilbert Hardy Space / Oscar F. Bandtlow / Oliver Jenkinson -- References / Oscar F. Bandtlow / Oliver Jenkinson -- 3.1. Introduction / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.2. Transfer Operators and Determinants / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.3. Determining the Escape Rate / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.4. Determining the Escape Measure / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.5. Example / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.5.1. Escape Rate / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 3.5.2. Escape Measure / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- References / Oscar F. Bandtlow / Oliver Jenkinson / Mark Pollicott -- 4.1. Introduction / Ranil Basnayake / Erik M. Bollt -- 4.2. Classical Optical Flow Method / Ranil Basnayake / Erik M. Bollt -- 4.2.1. Euler-Lagrange Equations / Ranil Basnayake / Erik M. Bollt -- 4.2.2. Solution to the Optical Flow Problem / Ranil Basnayake / Erik M. Bollt -- 4.3. Stream Function Method / Ranil Basnayake / Erik M. Bollt -- 4.4. Multi-time Step Method / Ranil Basnayake / Erik M. Bollt -- 4.5. Scientific Priors / Ranil Basnayake / Erik M. Bollt -- 4.6. Results from Multi-time Step Method / Ranil Basnayake / Erik M. Bollt -- 4.6.1. Synthetic Data / Ranil Basnayake / Erik M. Bollt -- 4.6.2. Oceanographic Data Set / Ranil Basnayake / Erik M. Bollt -- 4.7. Mixing and Transport Barriers / Ranil Basnayake / Erik M. Bollt -- 4.8. Conclusion / Ranil Basnayake / Erik M. Bollt -- References / Ranil Basnayake / Erik M. Bollt -- 5.1. Introduction / Christopher Bose / Rua Murray -- 5.1.1. Nonsingular Open Dynamical Systems / Christopher Bose / Rua Murray -- 5.1.2. Escape, Conditionally Invariant Measures and Their Supports / Christopher Bose / Rua Murray -- 5.1.3. Conditional Transfer Operators and the Multiplicity of ACCIMs / Christopher Bose / Rua Murray -- 5.2. Convex Optimisation for the ACCIM Problem / Christopher Bose / Rua Murray -- 5.2.1. Moment Formulation of the ACCIM Problem / Christopher Bose / Rua Murray -- 5.2.2. Convex Duality for Problem (Pn, α) / Christopher Bose / Rua Murray -- 5.2.3. Domain Reduction and Dual Optimality Conditions / Christopher Bose / Rua Murray -- 5.3. MAXENT Procedure for Approximating ACCIMs / Christopher Bose / Rua Murray -- 5.3.1. Piecewise Constant Test Functions and Domain Reduction / Christopher Bose / Rua Murray -- 5.3.2. Iterative Solution of the Optimality Equations / Christopher Bose / Rua Murray -- 5.3.3. Sketch Proof of Convergence of the Fixed Point Iteration / Christopher Bose / Rua Murray -- 5.3.4. Examples / Christopher Bose / Rua Murray -- 5.4. Concluding Remarks / Christopher Bose / Rua Murray -- References / Christopher Bose / Rua Murray -- 6.1. Introduction / Henk Bruin -- 6.2. Proof of Theorem 7.3 / Henk Bruin -- 6.2.1. Finding Convenient Coordinates / Henk Bruin -- 6.2.2. Distortion Results / Henk Bruin -- 6.2.3. Growth of ak and ak at Different Points / Henk Bruin -- 6.2.4. Main Proof / Henk Bruin -- References / Henk Bruin -- 7.1. Introduction / L.A. Bunimovich / B.Z. Webb -- 7.2. Open and Closed Dynamical Systems / B.Z. Webb / L.A. Bunimovich -- 7.3. Piecewise Linear Functions / B.Z. Webb / L.A. Bunimovich -- 7.4. Nonlinear Estimates / B.Z. Webb / L.A. Bunimovich -- 7.5. Improved Escape Estimates / B.Z. Webb / L.A. Bunimovich -- 7.6. Conclusion / B.Z. Webb / L.A. Bunimovich -- References / B.Z. Webb / L.A. Bunimovich -- 8.1. Introduction / Mark F. Demers -- 8.1.1. Preliminaries / Mark F. Demers -- 8.2. Setting and Results / Mark F. Demers -- 8.2.1. Classes of Dispersing Billiards / Mark F. Demers -- 8.2.2. Admissible Holes / Mark F. Demers -- 8.2.3. Transfer Operator / Mark F. Demers -- 8.2.4. Main Results / Mark F. Demers -- 8.3. Analytical Framework / Mark F. Demers -- 8.3.1. Representation of Admissible Stable Curves / Mark F. Demers -- 8.3.2. Norms / Mark F. Demers -- 8.3.3. Uniform Properties of T / Mark F. Demers -- 8.3.4. Verifying (A1)-(A5) for Our Classes of Maps / Mark F. Demers -- 8.3.5. Properties of the Banach Spaces / Mark F. Demers -- 8.4. Extension to Open Systems / Mark F. Demers -- 8.4.1. Complexity Bound and Proof of Proposition 8.1 / Mark F. Demers -- 8.4.2. Proof of Proposition 8.2 / Mark F. Demers -- 8.4.3. Proof of Theorems 8.1 and 8.2 / Mark F. Demers -- 8.5. Variational Principle / Mark F. Demers -- 8.5.1. Definition of vH / Mark F. Demers -- 8.5.2. Review: Young Towers with Holes / Mark F. Demers -- 8.5.3. Proof of Theorem 8.3 Assuming a Young Tower Respecting H / Mark F. Demers -- 8.5.4. Existence of a Young Tower Respecting the Hole / Mark F. Demers -- References / Mark F. Demers -- 9.1. Introduction / Gary Froyland / Kathrin Padberg-Gehle -- 9.2. Transfer Operators and Three Transport Problems / Gary Froyland / Kathrin Padberg-Gehle -- 9.2.1. Autonomous, Time-Independent, or Periodically Forced Dynamics / Gary Froyland / Kathrin Padberg-Gehle -- 9.2.2. Nonautonomous, Time-Dependent, or Aperiodically Forced Dynamics: Single Time Direction / Gary Froyland / Kathrin Padberg-Gehle -- 9.2.3. Nonautonomous, Time-Dependent, or Aperiodically Forced Dynamics: Both Time Directions / Gary Froyland / Kathrin Padberg-Gehle -- 9.3. Two Key Tools / Kathrin Padberg-Gehle / Gary Froyland -- 9.3.1. Building Block Operator / Kathrin Padberg-Gehle / Gary Froyland -- 9.3.2. Optimality Properties of Compact Self-Adjoint Operators on Hilbert Space / Gary Froyland / Kathrin Padberg-Gehle -- 9.4. Main Constructions and Results / Gary Froyland / Kathrin Padberg-Gehle -- 9.4.1. Autonomous Dynamics / Gary Froyland / Kathrin Padberg-Gehle -- 9.4.2. Nonautonomous or Time-Dependent Dynamics: Single Time Direction / Kathrin Padberg-Gehle / Gary Froyland -- 9.4.3. Nonautonomous or Time-Dependent Dynamics: Both Time Directions / Gary Froyland / Kathrin Padberg-Gehle -- 9.5. Further Discussion / Kathrin Padberg-Gehle / Gary Froyland -- 9.5.1. Single- vs |
| Summary |
This book is comprised of selected research articles developed from a workshop onErgodic Theory, Probabilistic Methods and Applications, held in April 2012 at the BanffInternational Research Station. It contains contributions from world leading expertsin ergodic theory, dynamical systems, numerical analysis, fluid dynamics, and networks. The volume will serve asa valuable reference for mathematicians, physicists, engineers, physical oceanographers, atmospheric scientists, biologists, and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open, coherent, or non-equilibrium behavior |
| Analysis |
calculus |
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optimalisatie |
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optimization |
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wiskunde |
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mathematics |
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waarschijnlijkheidstheorie |
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probability theory |
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stochastische processen |
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stochastic processes |
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optimalisatiemethoden |
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optimization methods |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed May 12, 2014) |
| Subject |
Ergodic theory.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Ergodic theory
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| Form |
Electronic book
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| Author |
Bahsoun, Wael, editor
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Bose, Christopher, editor
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Froyland, Gary, editor
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| ISBN |
9781493904198 |
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1493904191 |
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1493904183 |
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9781493904181 |
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