Abstract
This chapter is concerned with countable state Markov shifts. The first problem is to extend the Perron-Frobenius theory to nonnegative, countably infinite matrices. There are several difficulties. Countable matrices are classified by recurrence properties. There are three classes: positive recurrent, null recurrent and transient. The corresponding version of the Perron-Frobenius Theorem is successively weakened for each class. The necessary matrix theory is treated in the first section. The treatment is complete and there are a number of examples.KeywordsFinite TypeTopological EntropyNonnegative MatrixMaximal MeasureBorel Probability MeasureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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