Logs are rotated based on a max file size in AppMon. If you look into the server.config.xml file (or the relevant file for any other AppMon components) you can find a loggingconfig entry that has settings for the max file size and how many old files to continue storing. By default in mine it looks like the default for the standard Server logs is a max of 5 log files stored at once with a maz size of ~10MB:
<loggingconfig path="../log/collector/Dynatrace Collector" console="INFO" maxfiles="5" level="ALL" correlationmaxfiles="2" maxbytes="10485760" correlationmaxbytes="31457280" html="false" append="true" />
I wouldn't change these defaults without a good reason, you shouldn't need to do any manual management of log files.