Renormalization in Lorenz maps -- completely invariant sets and periodic orbits (Q6611883)

This work addresses the dynamics of expanding Lorenz maps, a class of interval maps associated with Poincaré sections of the Lorenz attractor. The authors examine the relationship between periodic points and completely invariant sets, and renormalizations of the Lorenz maps, employing both analytical and symbolic methods. A key contribution is the identification of conditions under which renormalizations correspond to completely invariant sets, supported by an algorithm to detect these cases. The paper claims to correct statements made in the existing literature, offering a more comprehensive description of the dynamical behavior of Lorenz maps.