Nonexistence of Chaotic Solutions of Nonlinear Differential Equations

TL;DR

This paper clarifies misconceptions in dynamical systems and fluid dynamics, emphasizing the importance of correct interpretation of computational results to ensure sound progress in understanding nonlinear differential equations.

Contribution

It highlights common misunderstandings and advocates for proper interpretation of computational findings in dynamical systems and fluid dynamics.

Findings

Misinterpretations of computational results are widespread.

Correct understanding is crucial for progress in nonlinear dynamics.

The paper calls for improved analytical approaches.

Abstract

We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely misinterpreted, and even viewed as "laws" by some. This paper hopes to stimulate appropriate corrections and to realign thinking, with the overall goal being sound future progress in dynamical systems and fluid dynamics.