TY - JOUR
T1 - Stable Minimality of Expanding Foliations
AU - Núñez, Gabriel
AU - Rodriguez Hertz, Jana
N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - We prove that generically in Diffm1(M), if an expanding f-invariant foliation W of dimension u is minimal and there is a periodic point of unstable index u, the foliation is stably minimal. By this we mean there is a C1-neighborhood U of f such that for all C2-diffeomorphisms g∈ U, the g-invariant continuation of W is minimal. In particular, all such g are topologically mixing. Moreover, all such g have a hyperbolic ergodic component of the volume measure m which is essentially dense. This component is, in fact, Bernoulli. We provide new examples of diffeomorphisms with stably minimal expanding foliations which are not partially hyperbolic.
AB - We prove that generically in Diffm1(M), if an expanding f-invariant foliation W of dimension u is minimal and there is a periodic point of unstable index u, the foliation is stably minimal. By this we mean there is a C1-neighborhood U of f such that for all C2-diffeomorphisms g∈ U, the g-invariant continuation of W is minimal. In particular, all such g are topologically mixing. Moreover, all such g have a hyperbolic ergodic component of the volume measure m which is essentially dense. This component is, in fact, Bernoulli. We provide new examples of diffeomorphisms with stably minimal expanding foliations which are not partially hyperbolic.
KW - Minimal foliation
KW - Stable ergodicity
KW - Stable minimality
UR - http://www.scopus.com/inward/record.url?scp=85089859406&partnerID=8YFLogxK
U2 - 10.1007/s10884-020-09884-x
DO - 10.1007/s10884-020-09884-x
M3 - Artículo
AN - SCOPUS:85089859406
SN - 1040-7294
VL - 33
SP - 2075
EP - 2089
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
IS - 4
ER -