Dynamic System Seminar——Symbolic extensions for 3-dimensional diffeomorphisms

2020-01-07 10:00-11:00 Room 1303, Science Building No.1

Abstract: The coding of dynamical system  is  a way to simulate chaotic behavior by symbolic dynamics. We prove that every  C^r diffeomorphism with r>1 on a three-dimensional  manifold  admits symbolic extensions, i.e.  topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of  Downarowicz  and  Newhouse in dimension three.