On knots in overtwisted contact structures

We prove that each overtwisted contact structure has knot types that arerepresented by infinitely many distinct transverse knots all with the sameself-linking number. In some cases, we can even classify all such knots. Wealso show similar results for Legendrian knots and prove a "folk" resultconcerning loose transverse and Legendrian knots (that is knots withovertwisted complements) which says that such knots are determined by theirclassical invariants (up to contactomorphism). Finally we discuss how theseresults partially fill in our understanding of the "geography" and "botany"'problems for Legendrian knots in overtwisted contact structures, as well asmany open questions regarding these problems.