eberhard hopf riemann surfaces negative curvature markov chains form common context applications probability theory ergodic theory fruitful connections harmonic analysis lie theory representation theory lattices algebraic groups number theory theory diophantine approximations l functions ergodic transformations ergodic theory often concerned '''ergodic transformations''' intuition behind transformations act given set thorough job stirring elements set eg set quantity hot oatmeal bowl spoonful syrup
Formal science Mathematics Pure mathematics Probability theory Ergodic theory