[CentOS] Cronjob script with date stamp?

I have a cron job that calls a shell script - the script invokes dump.

I'd like to do two things:

- Have the script dump the results of the job to a text file.  I tried 
this with /path/to/dump my switches -v >> /home/me/dump.log

But that just produced an empty file.


- Have the dump file be date-stamped with the date it was executed.  Right 
now, I manually edit the script to change the filename to the date the 
dump will be taken.


To get a differential dump, would I have dump produce its output to the 
same file each time?   I would not want to overwright the existing 
contents.  I'm currently dumping to a file on an external hard drive, but 
will eventually go to tape.

Thanks for feedback.

Scott