@article {6, title = {Studying the basin of convergence of methods for computing periodic orbits}, journal = {International Journal of Bifurcation and Chaos (IJBC)}, volume = {21}, year = {2011}, pages = {1-28}, abstract = {Starting from the well-known Newton{\textquoteright}s fractal which is formed by the basin of convergence of Newton{\textquoteright}s method applied to a cubic equation in one variable in the field ℂ, we were able to find methods for which the corresponding basins of convergence do not exhibit a fractal-like structure. Using this approach we are able to distinguish reliable and robust methods for tackling a specific problem. Also, our approach is illustrated here for methods for computing periodic orbits of nonlinear mappings as well as for fixed points of the Poincar{\'e} map on a surface of section.}, doi = {10.1142/S0218127411029653}, author = {M. G. Epitropakis and M. N. Vrahatis} }