$(".dropdown ul li").live("mouseover", function() {
alert('mouseover works');
});

$(".dropdown ul li").on("mouseover", function() {
alert('mouseover works');
});

$(".static-parent").on("event1 event2", ".dynamic-child", function() {

$(".dropdown").on("mouseover", "li", function() {
   alert('mouseover works!!!!!!!!!');
});

jQuery(function($) { // DOM is now ready and $ alias secured

    $(".dropdown").on("mouseover", "li", function() {
       alert('mouseover works!!!!!!!!!');
    });

});