Ratner's Theorems
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Ratner''s theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems grew out of Ratner''s earlier work on horocycle flows. The study of the dynamics of unipotent flows played decisive role in the proof of the Oppenheim conjecture by Margulis. Ratner''s theorems have guided key advances in the understanding of the dynamics of unipotent flows. Their later…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Ratner''s theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems grew out of Ratner''s earlier work on horocycle flows. The study of the dynamics of unipotent flows played decisive role in the proof of the Oppenheim conjecture by Margulis. Ratner''s theorems have guided key advances in the understanding of the dynamics of unipotent flows. Their later generalizations provide ways to both sharpen the results and extend the theory to the setting of arbitrary semisimple algebraic groups over a local field.