Space % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYt % UvgaiyaacqWFsectaaa!4667! $$ \mathcal{L} $$ (X) of local dynamical systems and the Filippov space A ceu(X)

Abstract

In the present paper, we establish a relationship between continuous local dynamical systems and spaces of the class A ceu(X) of the Filippov theory. We suggest a construction method for a space of the class A ceu(X) on the basis of a locally given dynamical system and conversely, a dynamical system is constructed locally in a specific way on the basis of a given space of the class A ceu(X). The suggested construction method provides a homeomorphism between the space of all local dynamical systems on a locally compact metric space X and the space A ceu(X). The obtained results generalize the Filippov theory to locally dynamical systems.