LARGE ENTROPY MEASURES OF H ´ ENON-LIKE MAPS
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Ushu maqolada H´ enon akslantirishlari uchun berilgan invariant ergodik o‘lchovlarning Lyapunov
eksponentalari entropiyaga qo‘yilagn ma’lum shart asosida o‘rganildi. Boshqacha aytganda, d +
p−1 < d
shartni qanoatlantiruvchi f H´ enon akslantirishi berilgan bo‘lsin. Agar ν ergodik o‘lchov entropiyasi
uchun h ν (f) > logd +
p−1
o‘rinli bo‘lsa, ν o‘lchovga bog‘liq kamida p ta musbat Lyapunov
eksponentalari topilib, quyidan (h ν (f) − logd +
p−1 )/2k bilan chegaralangan ekanligi ko‘rsatilgan.
1. Tien-Cuong Dinh, Viet-Anh Nguyen and Nessim Sibony. Dynamics of horizontal-like maps in higher
dimension. Advances in Mathematics, V.219, N.5, 2008, P.1689-1721.
2. Tien-Cuong Dinh and Nessim Sibony. Dynamics in several complex variables: endomorphisms of projective
spaces and polynomial-like mappings. Springer, Berlin, 2010, P.165-294.
3. Fabrizio Bianchi, Tien-Cuong Dinh and Karim Rakhimov. Monotonicity of dynamical degrees for H´ enon-
like and polynomial-like maps.Transactions of the American Mathematical Society, V.93, 2024, P.1-23.
4. Mikhael Gromov. On the entropy of holomorphic maps. Enseignement math, Manuscript, 2003, p.217-235.
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