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• W3100438106 abstract "We investigate the relations holding among generalized dimensions of invariant measures in dynamical systems and similar quantities defined by the scaling of global averages of powers of return times. Because of a heuristic use of Kac theorem, these latter have been used in place of the former in numerical and experimental investigations; to mark this distinction, we call them return time dimensions. We derive a full set of inequalities linking measure and return time dimensions and we comment on their optimality with the aid of two maps due to von Neumann -- Kakutani and to Gaspard -- Wang. We conjecture the behavior of return time dimensions in a typical system. We only assume ergodicity of the dynamical system under investigation." @default.
• W3100438106 created "2020-11-23" @default.
• W3100438106 creator A5048292536 @default.
• W3100438106 date "2009-12-05" @default.
• W3100438106 modified "2023-10-13" @default.
• W3100438106 title "The Global Statistics of Return Times: Return Time Dimensions Versus Generalized Measure Dimensions" @default.
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• W3100438106 doi "https://doi.org/10.1007/s10955-009-9894-y" @default.
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