Geodesic flow on Riemannian manifolds

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A naive question. I see many research papers on geodesic flows on Riemannian manifolds. Some of them try for instance to show that they are ergodic. It is probably a very broad question but could you give me some general ideas about why is the study of this flow important? And what does the fact that it is ergodic tells us?




differential-geometry ergodic-theory geodesic




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    A naive question. I see many research papers on geodesic flows on Riemannian manifolds. Some of them try for instance to show that they are ergodic. It is probably a very broad question but could you give me some general ideas about why is the study of this flow important? And what does the fact that it is ergodic tells us?




    differential-geometry ergodic-theory geodesic




    share|cite|improve this question





















      up vote
      6
      down vote

      favorite









      up vote
      6
      down vote

      favorite











      A naive question. I see many research papers on geodesic flows on Riemannian manifolds. Some of them try for instance to show that they are ergodic. It is probably a very broad question but could you give me some general ideas about why is the study of this flow important? And what does the fact that it is ergodic tells us?




      differential-geometry ergodic-theory geodesic




      share|cite|improve this question











      A naive question. I see many research papers on geodesic flows on Riemannian manifolds. Some of them try for instance to show that they are ergodic. It is probably a very broad question but could you give me some general ideas about why is the study of this flow important? And what does the fact that it is ergodic tells us?





      differential-geometry ergodic-theory geodesic





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 14 at 23:44









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