Dynamical Systems and Random Processes.

Cover -- Title page -- Contents -- Preface -- Chain recurrence and strong chain recurrence on uniform spaces -- 1. Introduction -- 2. Definitions and background -- 3. Barrier functions -- 4. The Conley and Aubry-Mather chain-relations -- 5. Lyapunov functions -- 6. Conley and Aubry-Mather relations for uniform spaces -- References -- Towards the prediction of critical transitions in spatially extended populations with cubical homology -- 1. Introduction -- 2. Background -- 3. Results -- 4. Discussion -- 5. Acknowledgements -- References -- Relating singularly perturbed rational maps to families of entire maps -- 1. Introduction -- 2. Basic properties of the functions -- 3. Dynamical Plane -- 4. Parameter Plane -- References -- Stability of Cantor Julia sets in the space of iterated elliptic functions -- 1. Introduction -- 2. Preliminary background and definitions -- 3. Julia sets -- 4. Rhombic square lattices -- 5. Triangular lattices and stability -- 6. Real rectangular lattices -- 7. Hyperbolic components of \M with connected Julia sets -- References -- Pressure and escape rates for random subshifts of finite type -- 1. Introduction -- 2. Background and notation -- 3. Pressure of random SFTs -- 4. Repeat probabilities -- 5. Moment bounds -- 6. Bounds on pressure -- 7. Connection between pressure and escape rate -- Acknowledgments -- References -- On the complexity function for sequences which are not uniformly recurrent -- 1. Introduction and definitions -- 2. Definitions -- 3. Proofs -- References -- Definitions and properties of entropy and distance for regular languages -- 1. Introduction -- 2. Background -- 3. Language Entropy -- 4. Entropy Distances -- 5. Jaccard Distances -- 6. Conclusion -- References -- Good and Bad Functions for Bad Processes -- 1. Introduction -- 2. Processes Depending on a Map.

3. Processes Depending on a Group of Maps -- References -- Isomorphisms of cubic rational maps that preserve an infinite measure -- 1. Introduction -- 2. Background and Notation -- 3. Degree 3 Boole Transformations -- 4. Symmetric Degree 3 Boole Transformations -- References -- Orbit classification and asymptotic constants for -symmetric covers -- 1. Introduction and Results -- 2. Background on translation surfaces -- Finite \slz orbits on tori -- 3. Parameter spaces of cyclic covers -- 4. Asymptotic formulas for branched covers -- 5. Asymptotic constants and parameter space geometry. -- 6. Teichmüller curves and moduli space -- 7. Cylinder decompositions of -symmetric forms -- 8. Illumination and non illumination -- 9. Asymptotic constants -cylinders, generic case -- 10. Asymptotic constants -cylinders, finite orbit case -- 11. Asymptotic constants -saddle connections -- 12. Questions and Comments -- References -- On the collision manifold of coorbital moons -- 1. Coorbital Model -- 2. Solar-system formation -- 3. Cors and Hall Coordinates -- 4. Change of Variables into Polar Coordinates -- 5. Collision Manifold -- 6. Flow at Binary Collision -- References -- Multivariate random fields and their zero sets -- 1. Introduction -- 2. Formulas for the expected ( - )-dimensional area of \Cal{ }(\Fv_{ }) -- 3. The Gaussian measure Γ^{ }ₓ on ₓ⊕\Cal{ }( ₓ, ₓ) -- 4. Heat asymptotics and zero set asymptotics -- 5. Other directions -- Appendix A. Remarks on ( , ) -- References -- Back Cover.

This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13-15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.