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 infinite, 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.
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Return map of
Topological cylinders
Behavior of the orbits outside and inside of the planes
Behavior at Theorems B and C