Relaxing in stressful circumstances comes down to good, deep, rythmic breathing and you can learn that without paying ungodly amounts of cash. But I've never tried systema so I really can't truly say what it's all about I'll have to check it out one day.
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Member of DaJoGen MMA school under Dave Hagen and Team Chaos fight team under Denver Mangiyatan and Chris Toquero, ran out of Zanshin Martial Arts in Salem Oregon: http://www.zanshinarts.org/Home.aspx,