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A multidimensional version of the Li–Yorke cycle coexisting theorem [Li, T.-Y. and Yorke, J.A. “Period three implies chaos”, Am. Math. Monthly, 82, 985–992] is established for certain (e.g. expansive) maps. The related fixed- and periodic-point theorems are developed in R n . Implications of 3-orbits are discussed.
Supported by the Council of Czech Government (J14/98:153100011) and by the Grant No. 201-00-0768 of the Grant Agency of Czech Republic.
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