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ON LOOPS IN THE HYPERBOLIC LOCUS OF THE COMPLEX HENON MAP
 

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 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.
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
:
x

  

Source: Arai, Zin - Department of Mathematics, Kyoto University

 

Collections: Mathematics