pax
Pax is the best tool for this task. It's POSIX's replacement for cpio and tar (and unlike tar it includes a pass-through mode, not just archive creation and extraction). Sadly, it's omitted from the default installation in some Linux distributions, but it's only an apt-get/yum/emerge/… invocation away.
Pax has a limitation: recently modified directories will be copied even if they contain no file to be copied. You can remove empty directory afterwards (unless there are pre-existing empty directories in the destination that you want to preserve).
cd /path/to/source pax -rw -pp -T 201409080000 . /path/to/destination/ find /path/to/destination/ -depth -type d -exec rmdir {} + I'll mention other ways, that can be adapted to similar but not identical use cases where pax doesn't have a filter.
Zsh
Use the glob qualifier m to match files by their modification time (e.g. m-10 for files modified in the past 10 days; you can use other units instead), and . to match regular files. The history modifier h retains the directory part of the file name.
cd /path/to/source for x in **/*(.m-10); do mkdir -p -- $x:h cp -p -- $x /path/to/destination/$x done Alternatively, you can use the zmv function to copy files matched by a wildcard expression. There's no built-in way to create the destination directory, so I provide a function to do it.
autoload -U zmv mkdir_cp () { mkdir -p -- ${(P)#}:h cp -- $@ } cd /path/to/source zmv -p mkdir_cp -Q '**/*(.m-10)' '/path/to/destination/$f' POSIX find
With find, you can use -mtime -10 to match files modified in the past 10 days, or -newer reference_time to match files modified after reference_files.
touch -t 201409080000 /tmp/reference_time cd /path/to/source find . -type f -newer /tmp/reference_time -exec sh -c ' mkdir -p /path/to/destination/"${0%/*}" cp "$0" "/path/to/destination/$0" ' {} \; 
