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 -