Lyapunov exponent is widely used in natural science to find chaotic signal, but its existence seldom discussed. In the present paper, we consider problem of whether set points at which fails exist, called irregular set, has positive Lebesgue measure. The only known example with measure a figure-8 attractor by work Ott and Yorke (Phys Rev 78, 056203, 2008), whose key mechanism (homoclinic loop) ...

ABSTRACT The standard cosmological model Lambda Cold Dark Matter (LCDM) assumes a global expanding space–time of infinite extent around us. But such idea is inconsistent with the observed cosmic acceleration unless we advocate for existence mysterious dark energy (DE) or constant (Λ). Here, argue instead that our Universe has very large but finite regular mass M, without need to invoke DE Λ. A ...