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Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
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摘要 Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems. Ma(n)é conjectured that every minimal measure in the generic Lagrangian systems is by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems.
出处 《Science China Mathematics》 SCIE 2006年第12期1864-1866,共3页 中国科学:数学(英文版)
关键词 MINIMAL PROBABILITY measure uniquely ergodic Mather theory Lagrangian systems. minimal probability measure, uniquely ergodic, Mather theory, Lagrangian systems.
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参考文献4

  • 1[1]Mather J.Action minimizing invariant measures for positive definite Lagrangian systems.Math Z,1991,207:169-207 被引量:1
  • 2[2]Mather J.Variational construction of connecting orbits.Ann Inst Fourier,1993,43:1349-1386 被引量:1
  • 3[3]Ma(n)é R.Generie properties and problem of minimizing measures of Lagrangian systems.Nonlinearity,1996,9:273-310 被引量:1
  • 4[4]Ma(n)é R.Lagrangian flows:the dynamical systems (Montevido 1995).Pitman Research Notes in Math,1996,362:120-131 被引量:1

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