TY - GEN

T1 - Measure theory and geometric topology in dynamics

AU - Rodriguez Hertz, Federico Juan

PY - 2010/12/1

Y1 - 2010/12/1

N2 - In this survey we shall present some relations between measure theory and geometric topology in dynamics. One of these relations comes as follows, on one hand from topological information of the system, some structure should be preserved by the dynamics at least in some weak sense, on the other hand, measure theory is soft enough that an invariant geometric structure almost always appears along some carefully chosen invariant measure. As an example, we have the known result that in dimension 2 the system has asymptotic growth of hyperbolic periodic orbits at least equal to the largest exponent of the action in homology.

AB - In this survey we shall present some relations between measure theory and geometric topology in dynamics. One of these relations comes as follows, on one hand from topological information of the system, some structure should be preserved by the dynamics at least in some weak sense, on the other hand, measure theory is soft enough that an invariant geometric structure almost always appears along some carefully chosen invariant measure. As an example, we have the known result that in dimension 2 the system has asymptotic growth of hyperbolic periodic orbits at least equal to the largest exponent of the action in homology.

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M3 - Conference contribution

AN - SCOPUS:84877901896

SN - 9814324302

SN - 9789814324304

T3 - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

SP - 1760

EP - 1776

BT - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

T2 - International Congress of Mathematicians 2010, ICM 2010

Y2 - 19 August 2010 through 27 August 2010

ER -