Constructing Multidimensional Dynamical Systems with Positive Lyapunov Exponents

Sammanfattning: In this thesis we adapt Marcelo Viana's general construction of smooth transformations exhibiting non-uniform expansion in several dimensions. In our construction we, instead of coupling with a quadratic map, as Viana did, derive the expansion from a mapping with a cubic critical point. Further, we discuss how the argument can be extended and expansion derived from certain mappings with a critical point of arbitrarily high (odd) degree. We also discuss the issues in trying to use Viana's method with the double standard map as our source of non-uniform expansion.