@article{1433703,
      recid = {1433703},
      author = {Hawkins, Jane,},
      title = {Ergodic dynamics : from basic theory to applications /},
      pages = {1 online resource :},
      abstract = {This textbook provides a broad introduction to the fields  of dynamical systems and ergodic theory. Motivated by  examples throughout, the author offers readers an  approachable entry-point to the dynamics of ergodic  systems. Modern and classical applications complement the  theory on topics ranging from financial fraud to virus  dynamics, offering numerous avenues for further inquiry.  Starting with several simple examples of dynamical systems,  the book begins by establishing the basics of measurable  dynamical systems, attractors, and the ergodic theorems.  From here, chapters are modular and can be selected  according to interest. Highlights include the  PerronFrobenius theorem, which is presented with proof and  applications that include Google PageRank. An in-depth  exploration of invariant measures includes ratio sets and  type III measurable dynamical systems using the von Neumann  factor classification. Topological and measure theoretic  entropy are illustrated and compared in detail, with an  algorithmic application of entropy used to study the  papillomavirus genome. A chapter on complex dynamics  introduces Julia sets and proves their ergodicity for  certain maps. Cellular automata are explored as a series of  case studies in one and two dimensions, including Conways  Game of Life and latent infections of HIV. Other chapters  discuss mixing properties, shift spaces, and toral  automorphisms. Ergodic Dynamics unifies topics across  ergodic theory, topological dynamics, complex dynamics, and  dynamical systems, offering an accessible introduction to  the area. Readers across pure and applied mathematics will  appreciate the rich illustration of the theory through  examples, real-world connections, and vivid color graphics.  A solid grounding in measure theory, topology, and complex  analysis is assumed; appendices provide a brief review of  the essentials from measure theory, functional analysis,  and probability.},
      url = {http://library.usi.edu/record/1433703},
      doi = {https://doi.org/10.1007/978-3-030-59242-4},
}