TY - JOUR
T1 - Another proof of the averaging principle for fully coupled dynamical systems with hyperbolic fast motions
AU - Kifer, Yuri
PY - 2005/12
Y1 - 2005/12
N2 - In the study of systems which combine slow and fast motions which depend on each other (fully coupled setup) whenever the averaging principle can be justified this usually can be done only in the sense of L1- convergence on the space of initial conditions. When fast motions are hyperbolic (Axiom A) flows or diffeomorphisms (as well as expanding endomorphisms) for each freezed slow variable this form of the averaging principle was derived in [19] and [20] relying on some large deviations arguments which can be applied only in the Axiom A or uniformly expanding case. Here we give another proof which seems to work in a more general framework, in particular, when fast motions are some partially hyperbolic or some nonuniformly hyperbolic dynamical systems or nonuniformly expanding endomorphisms.
AB - In the study of systems which combine slow and fast motions which depend on each other (fully coupled setup) whenever the averaging principle can be justified this usually can be done only in the sense of L1- convergence on the space of initial conditions. When fast motions are hyperbolic (Axiom A) flows or diffeomorphisms (as well as expanding endomorphisms) for each freezed slow variable this form of the averaging principle was derived in [19] and [20] relying on some large deviations arguments which can be applied only in the Axiom A or uniformly expanding case. Here we give another proof which seems to work in a more general framework, in particular, when fast motions are some partially hyperbolic or some nonuniformly hyperbolic dynamical systems or nonuniformly expanding endomorphisms.
KW - Averaging principle
KW - Hyperbolic attractors
UR - http://www.scopus.com/inward/record.url?scp=28444436624&partnerID=8YFLogxK
U2 - 10.3934/dcds.2005.13.1187
DO - 10.3934/dcds.2005.13.1187
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AN - SCOPUS:28444436624
SN - 1078-0947
VL - 13
SP - 1187
EP - 1201
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 5
ER -