Responsive design via an iframe for ArcGIS Java Script API 3.2

You can use this code for resizing the map automatically:

 //resize the map when the browser resizes - view the 'Resizing and repositioning the map' section in
              //the following help topic for more details http://help.esri.com/EN/webapi/javascript/arcgis/help/jshelp_start.htm#jshelp/inside_guidelines.htm      
              var resizeTimer;
              dojo.connect(map, 'onLoad', function(theMap) {
                dojo.connect(dijit.byId('map'), 'resize', function() { //resize the map if the div is resized
                  clearTimeout(resizeTimer);
                  resizeTimer = setTimeout(function() {
                    map.resize();
                    map.reposition();
                  }, 500);
                });
              });

            }