I can't attempt to reproduce your results because I do not have access to those OS's. But, you could investigate further by showing us the contents of $0: 
use strict;
use warnings;

print "script = >>>$0<<<\n";
my $log_file = (split /\./, $0)[0] . '.log';
print $log_file, "\n";

[download]
Basic debugging checklist

In reply to Re: Different behavior when parsing $0 on Solaris and Win32 by toolic
in thread Different behavior when parsing $0 on Solaris and Win32 by dirac

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