Explore the dynamics of Chebyshev's method applied to polynomials, focusing on cubic polynomials and their Julia sets. Investigate the degree of Chebyshev's method for different polynomial types, and examine the connectivity of Julia sets for unicritical, non-generic, and generic cubic polynomials. Learn about the parametrization of rational maps arising from Chebyshev's method applied to non-unicritical and generic cubic polynomials, and discover the conditions for connected Julia sets in this family of maps.