Theoretical Investigation of the Physics ofv Chaos in Fourth and Higher Dimensions

The possible existence of spatial dimensions beyond the known 3-dimensional space is a question of great importance in Theoretical Physics. Our approach is to look for the signature of extra spatial dimensions by simulating the apparent 3-D chaotic dynamical phenomena that could result from the existence of the extra dimensions. In 1975, Li and Yorke formulated the concept of Dynamical Chaos, and gave a condition for it in scalar difference equations: the “period three implies chaos” result. Subsequently other researchers have generalized the Li and Yorke definition of chaos to difference equations in Rⁿ and formulated higher dimensional conditions ensuring its existence, specifically the “snap-back repeller” condition of Marotto and its counterpart for saddle points. In this paper, we utilize the Feynman Path Integral approach, implemented with computer codes in Python and Fortran programming languages, to simulate generalized chaos. We propose possible laboratory experiments that might help to check the validity of our theoretical results. The possible link of an extra spatial dimension to the existence of Dark Matter is also discussed.