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Nonlinear Dynamics And Statistics,New
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All Models Are Lies. 'The Earth Orbits The Sun In An Ellipse With The Sun At One Focus' Is False, But Accurate Enough For Almost All Purposes. This Book Describes The Current State Of The Art Of Telling Useful Lies About Timevarying Systems In The Real World. Specifically, It Is About Trying To 'Understand' (That Is, Tell Useful Lies About) Dynamical Systems Directly From Observa Tions, Either Because They Are Too Complex To Model In The Conventional Way Or Because They Are Simply Illunderstood. B(:Cause It Overlaps With Conventional Timeseries Analysis, Building Mod Els Of Nonlinear Dynamical Systems Directly From Data Has Been Seen By Some Observers As A Somewhat Illinformed Attempt To Reinvent Timeseries Analysis. The Truth Is Distinctly Less Trivial. It Is Surely Impossible, Except In A Few Special Cases, To Recreate Newton'S Astonishing Feat Of Writing A Short Equation That Is An Excellent Description Of Realworld Phenomena. Real Systems Are Connected To The Rest Of The World; They Are Noisy, Non Stationary, And Have Highdimensional Dynamics; Even When The Dynamics Contains Lowerdimensional Attractors There Is Almost Never A Coordinate System Available In Which These At Tractors Have A Conventionally Simple Description.
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