The course is suitable for the M.Sc students working on their thesis and for Ph.D student. The content of this mini course is:

1. Absolutely continuous measure (1 hour),
2. Anosov-Katok method and extreme examples in dynamic (3 hours),
2. One dimensional transversality condition (2 hours),
4. Why Transversality condition implies the existence of ACIP (3 hours),

The references are:

• Y K. Oliveira and M. Viana, Foundation of ergodic theory, Cambridge University Press. February 2016.
• Y M. Tsujii, Fat solenoidal attractors, Nonlinearity, 14, (2001),1011-1027.
• Y B. Fayad and A. Katok Constructions in elliptic dynamics Ergod. The. Dynam. Syst., 24, (2004), 1477-1520.

Supplementary information about the course:

• Y Research area: Dynamical Systems,
• Y MSC: 37XX,
• Y Keywords: Attractor, Transversality, ACIP.