BIRTH OF AN ARBITRARY NUMBER OF T-SINGULARITIES IN 3D PIECEWISE SMOOTH VECTOR FIELDS

摘要

The T-singularity (invisible two-fold singularity) is one of the most intriguing objects in the study of 3D piecewise smooth vector fields. The occurrence of just one T-singularity already arouses the curiosity of experts in the area due to the wealth of behaviors that may arise in its neighborhood. In this work we show the birth of an arbitrary number, including in finite, of such singularities. Moreover, we are able to show the existence of an arbitrary number of limit cycles, hyperbolic or not, surrounding each one of these singularities.