Summary: ON LOOPS IN THE HYPERBOLIC LOCUS
OF THE COMPLEX H´ENON MAP
AND THEIR MONODROMIES
Abstract. We prove John Hubbard's conjecture on the topological
complexity of the hyperbolic horseshoe locus of the complex H´enon
map. In fact, we show that there exist several non-trivial loops in the
locus which generate infinitely many mutually different monodromies.
Furthermore, we prove that the dynamics of the real H´enon map is
completely determined by the monodromy of the complex H´enon map,
providing the parameter is contained in the hyperbolic horseshoe locus
of the complex H´enon map.
One of the motivations of this work is to give an answer to the conjec-
ture of John Hubbard on the topology of hyperbolic horseshoe locus of the
complex H´enon map
Ha,c : C2