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The Standard Map and a Probabilistic Conjecture
Author(s) -
Pustyl'nikov L.D.
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200011)219:1<181::aid-mana181>3.0.co;2-1
Subject(s) - mathematics , conjecture , probabilistic logic , statistics , combinatorics
Statistical properties of trajectories of a class of dynamical systems, which includes the standard map, are studied. In particular a well known conjecture is stated and its natural probabilistic analogue is defined in the framework of ergodic theory of random transformations. The main result is a proof of a probabilistic analogue of this conjecture.