The R language (http://www.r-project.org/) might lend itself well to your more intense mathematical demands. There are packages with specific to some of your concerns (e.g. Nonlinear Dynamics: http://cran.r-project.org/web/packages/tsDyn/).

That said, R is sort of a quirky language in some respects and does not tend to encourage as disciplined approach to software engineering as a language like Python.