" Markov process" . . . "recurrence; return times; hitting times; dynamical system; stationary process; Markov process; ergodicity; mixing; entropy; exponential law"@en . " entropy" . "2011-03-18+01:00"^^ . "A new limiting distribution of return times was found for typical processes derived from Bernoulli, Markov and other strongly mixing systems and adding machines. A zero-entropy process with the exponential limiting distribution was constructed."@en . " mixing" . . . . . "Byla nalezena nov\u00E1 limitn\u00ED distribuce dob n\u00E1vrat\u016F v typick\u00FDch procesech odvozen\u00FDch z Bernoulliovsk\u00FDch, Markovsk\u00FDch a jin\u00FDch siln\u011B m\u00EDchaj\u00EDc\u00EDch syst\u00E9m\u016F. Byl zkonstruov\u00E1n syst\u00E9m s nulovou entropi\u00ED, kter\u00FD m\u00E1 exponenci\u00E1ln\u00ED limitn\u00ED distribuci dob n\u00E1vrat\u016F."@cs . . "Typick\u00E9 doby n\u00E1vratu v dynamick\u00FDch syst\u00E9mech" . . " hitting times" . . . "KJB100750901" . . . . "2009-01-01+01:00"^^ . "Typical return times in dynamical systems"@en . "http://www.isvav.cz/projectDetail.do?rowId=KJB100750901"^^ . "recurrence" . "3"^^ . "0"^^ . "3"^^ . "Rekuren\u010Dn\u00ED vlastnosti dynamick\u00FDch syst\u00E9m\u016F a stacion\u00E1rn\u00EDch proces\u016F, zejm\u00E9na pak doby n\u00E1vratu a jejich limitn\u00ED rozlo\u017Een\u00ED jsou z\u00E1kladn\u00EDm pil\u00ED\u0159em ergodick\u00E9 teorie a teorie informace. V\u00FDsledky v t\u00E9to oblasti sahaj\u00ED od hlubok\u00FDch matematick\u00FDch v\u011Bt a\u017E po aplikace, jakou je nap\u0159\u00EDklad Lempel-Ziv algoritmus, pou\u017E\u00EDvan\u00FD p\u0159i kompresi dat ve form\u00E1tech pdf, giff, nebo tiff. P\u0159esto nen\u00ED st\u00E1le uspokojiv\u011B zodpov\u011Bzen\u00E1 ot\u00E1zka, jak vypad\u00E1 typick\u00E9 limitn\u00ED rozlo\u017Een\u00ED dob n\u00E1vratu v procesech odvozen\u00FDch z dan\u00E9ho dynamick\u00E9ho syst\u00E9mu. C\u00EDlem tohoto projektu je nal\u00E9zt tato rozlo\u017Een\u00ED a pomoc\u00ED nich klasifikovat zcela nov\u00FDm zp\u016Fsobem dynamick\u00E9 syst\u00E9my. Chceme t\u00E9\u017E zodpov\u011Bd\u011Bt, jak tato rozlo\u017Een\u00ED souvis\u00ED s dal\u0161\u00EDmi d\u016Fle\u017Eit\u00FDmi charakteristikami syst\u00E9mu, jako je entropie a mixuj\u00EDc\u00ED vlastnosti. V\u011B\u0159\u00EDme, \u017Ee p\u0159edpokl\u00E1dan\u00E9 v\u00FDsledky pomohou mimo jin\u00E9 l\u00E9pe pochopit a vy\u010D\u00EDslit \u00FA\u010Dinnost LZ algoritmu." . . "1"^^ . "Recurrence is one of the key concepts in topological dynamics, ergodic and information theories. Especially, limit distributions of return times in dynamical systems and stationary processes have been intensively studied. This field covers fundamental mathematical theorems as well as important apllications, e.g. Lempel-Ziv algorithm for data compression, practically used in format pdf, gif or tiff. However, the question about typical limit distributions of return times for processes derived from a given dynamical system is still open. The goal of this project is to find these typical distributions and establish corresponding classification of dynamical systems. This will be compared with other fundamental invariants, like entropy, and mixing properties. The expected results are believed to contribute to better understanding and evaluating efficiency of LZ algorithm."@en . "http://simu0292.utia.cas.cz/kupsa/"^^ . "0"^^ . . . "2012-05-25+02:00"^^ . " stationary process" . . " return times" . "2011-12-31+01:00"^^ . . " ergodicity" . . " dynamical system" .