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Let f:E -> E be a homeomorphism of the plane E. We define open sets P,called {\em pruning fronts} after the work of Cvitanovi\'c, for which it ispossible to construct an isotopy H: E x [0,1] -> E with open support containedin the union of f^{n}(P), such that H(*,0)=f(*) and H(*,1)=f_P(*), where f_Pis a homeomorphism under which every point of P is wandering. Applying thisconstruction with f being Smale's horseshoe, it is possible to obtain anuncountable family of homeomorphisms, depending on infinitely many parameters,going from trivial to chaotic dynamic behaviour. This family is a2-dimensional analog of a 1-dimensional universal family.

Pruning fronts and the formation of horseshoes