Loggers should:
private: never be accessible outside of its parent class. If another class needs to log something, it should instantiate its own logger.
static: not be dependent on an instance of a class (an object). When logging something, contextual information can of course be provided in the messages but the logger should be created at class level to prevent creating a logger along with each object.
(final|const): be created once and only once per class.
With the default regular expression LOG(?:GER)?:
public const logger:ILogger = LogUtil.getLogger(MyClass);
private static const LOG:ILogger = LogUtil.getLogger(MyClass);