#!/usr/bin/perl
use warnings;
use strict;

my %hash = (
            '.111' => 'Aaaa',
            '.222' => 'Bbbb',
            '.333' => 'Cccc'
           );

my %newhash = map { substr ($_, 2) => $hash{$_} } keys %hash;

for ( keys %newhash ) {
    print "$_ => ", $newhash{$_}, "\n";
}