I'm trying to get into the field of dynamical systems by (self) studying one-dimensional dynamics and circle homeomorphisms; for my guidance, I'm trying to assemble materials in this field that obey the following:
- Historical aspects (optional);
- A good topological approach;
- Without use Mathematica; for the numerical part, I'd like to use a more friendly programming language (that sounds quite subjective) like C, Python, FORTRAN, Perl, etc.
- Make a natural transition to more advanced topics (my goal is to get the road to topological dynamics);
I haven't included this one in my list (because I'm very sure that requires advanced treatment), but I'd love to get access to materials that relates dynamical systems to number theory, set theory and mathematical logic.
I have a background in abstract and linear algebra (in the level of Jacobson's Lectures in Algebra and Halmos's Finite Dimensional Vector Spaces), in general topology (Munkres's Topology, make transition to Engelking's General Topology) and set theory (Jech's Introduction to Set Theory).