 
Summary: ON LOOPS IN THE HYPERBOLIC LOCUS
OF THE COMPLEX H´ENON MAP
AND THEIR MONODROMIES
ZIN ARAI
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 nontrivial 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.
1. Introduction
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
C2
:
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