Finally I got the point. It's working, but my TESTING of it was WRONG.
Forward / back buttons are working well, however, back button to 'BLANK' home page was not working, because there simply wasn't rule to match blank parameter. Now it seems like this:
function handleChange(evt){
var path = evt.path;
switch(path) {
case '': // go home
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/index/uvod');
break;
case '!domov': // go home
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/index/uvod');
break;
case '!pridaj':
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/pridaj');
break;
case '!uprav':
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/uprav');
break;
case '!oprojekte':
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/index/oprojekte');
break;
case '!kontakt':
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/kontakt');
break;
case '!podmienky':
$('#ajax_ramec').html('<div style="margin-left: 50%; margin-top:50%; text-aligtn:center"><img src="'+baseURL+'/public/images/template/loading_small.gif" /></div>').load(baseURL+'/index/podmienky');
break;
}