Chaos in the Lorenz Equations:\\ a Computer-Assisted Proof

Chaos in the Lorenz Equations: a Computer-assisted Proof

A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer-assisted computations. As an application of these methods it is proven that for an explicit parameter value the Lorenz equations exhibit chaotic dynamics. Introduction The purpose of this...

Chaos in the Lorenz Equations : A Computer Assisted Proof ; Part III : Classical Parameter

Chaos in the Lorenz equations: A computer assisted proof. Part II: Details

Details of a new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with rigorous computer assisted computations. As an application of these methods it is proven that for some explicit parameter values the Lorenz equations exhibit chaotic dynamics.

learner autonomy in a computer-assisted project-based efl reading classroom

آموزش برمبنای ذخیره اطلاعات ، دانشجویان را به عنوان افرادی غیر متفکر وغیرقابل کنترل می پندارد . در همین راستا ، خواندن در سیستم آموزشی برمبنای ذخیره اطلاعات ، مهارتی پنداشته می شود که می توان آن را با یاد گرفتن انفعالی وجداگانه تعدادی از مهارتهای جزیی فراگرفت . درآن سو خواندن در سیستم آموزشی برمبنای طرح مسآله ،به عنوان رفتاری نقادانه تلقی می شود که از طریق آن می توان دنیای فرای کلمات را کشف کرد...

A Computer-Assisted Proof of Σ3-Chaos in the Forced Damped Pendulum Equation

The present paper is devoted to studying Hubbard’s pendulum equation ẍ+ 10ẋ+ sin(x) = cos(t) . By rigorous/interval methods of computation, the main assertion of Hubbard on chaos properties of the induced dynamics is lifted from the level of experimentally observed facts to the level of a theorem completely proved. A distinguished family of solutions is shown to be chaotic in the sense that on ...