The pentagram map is recurrent.
Schwartz, Richard Evan
Experimental Mathematics, Tome 10 (2001), p. 519-528 / Harvested from The Electronic Library of Mathematics
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Publié le : 2001-01-01
DOI : https://doi.org/10.1080/10586458.2001.10504671
EUDML-ID : urn:eudml:doc:50067 
@article{01799999,
     title = {The pentagram map is recurrent.},
     journal = {Experimental Mathematics},
     volume = {10},
     year = {2001},
     pages = {519-528},
     doi = {10.1080/10586458.2001.10504671},
     zbl = {1013.52003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/01799999}
}

Schwartz, Richard Evan. The pentagram map is recurrent.. Experimental Mathematics, Tome 10 (2001) pp. 519-528. doi : 10.1080/10586458.2001.10504671. http://gdmltest.u-ga.fr/item/01799999/