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• W2474982904 abstract "The 1999 paper by D. Lind and K. Schmidt on homoclinic points of a special class of dynamical systems—the so called algebraic ({{mathrm{mathbb {Z}^d}}})-actions—attracted a lot of interest to the study of homoclinic points. In the present paper we review the developments over the past 15 years. Major progress has been made in questions of existence of homoclinic points for ({{mathrm{mathbb {Z}^d}}})-actions. More recently, first results were obtained for actions of non-abelian discrete groups. Summable homoclinic points were successfully used in the computation of entropy and in the study of probabilistic properties of dynamical systems, e.g., Central Limit Theorems. Moreover, homoclinic points allow one to construct coding maps which link certain particle systems to algebraic dynamical systems." @default.
• W2474982904 created "2016-07-22" @default.
• W2474982904 creator A5000379071 @default.
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• W2474982904 date "2016-01-01" @default.
• W2474982904 modified "2023-09-27" @default.
• W2474982904 title "Homoclinic Points of Principal Algebraic Actions" @default.
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• W2474982904 doi "https://doi.org/10.1007/978-3-319-26883-5_4" @default.
• W2474982904 hasPublicationYear "2016" @default.
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