  Let $\{f_{a,b}\}$ be the (original) H\'enon family. In this paper, we show
that, for any $b$ near $0$, there exists a closed interval $J_b$ which contains
a dense subset $J'$ such that, for any $a\in J'$, $f_{a,b}$ has a quadratic
homoclinic tangency associated with a saddle fixed point of $f_{a,b}$ which
unfolds generically with respect to the one-parameter family $\{f_{a,b}\}_{a\in
J_b}$. By applying this result, we prove that $J_b$ contains a residual subset
$A_b^{(2)}$ such that, for any $a\in A_b^{(2)}$, $f_{a,b}$ admits the Newhouse
phenomenon. Moreover, the interval $J_b$ contains a dense subset $\tilde A_b$
such that, for any $a\in \tilde A_b$, $f_{a,b}$ has a large homoclinic set
without SRB measure and a small strange attractor with SRB measure
simultaneously.
  Dedicated to the memory of Floris Takens (Nov. 12, 1940 - Jun. 20, 2010).
