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Given clearance by your doctor, there should be no problem. Contact fighting may be off the list, but you can still participate in martial arts.
the Arni's Martial Arts have a rattan stick. while the other martial arts have no weapon
If you are talking about martial arts here is a list that should answer your question
AikidoSumoJuJutsuKenJutsuKendoIaidoNinjutsuJudoKarateKyudo
Martial Arts refers to the skills used in combat. Every country has martial arts and some originated in Japan, but not all of them.