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• W2460183023 abstract "We obtain a structurally stable family of smooth ordinary differential equations exhibiting heteroclinic tangencies for a dense subset of parameters. We use this to find vector fields C2-close to an element of the family exhibiting a tangency, for which the set of solutions with historic behaviour contains an open set. This provides an affirmative answer to Takens' last problem (Takens 2008 Nonlinearity 21 T33–6). A limited solution with historic behaviour is one for which the time averages do not converge as time goes to infinity. Takens' problem asks for dynamical systems where historic behaviour occurs persistently for initial conditions in a set with positive Lebesgue measure." @default.
• W2460183023 created "2016-07-22" @default.
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• W2460183023 creator A5043112874 @default.
• W2460183023 date "2017-04-03" @default.
• W2460183023 modified "2023-10-17" @default.
• W2460183023 title "On Takens’ last problem: tangencies and time averages near heteroclinic networks" @default.
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• W2460183023 doi "https://doi.org/10.1088/1361-6544/aa64e9" @default.
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