Xueting Tian

Dominated splitting and Pesin's entropy formula

Let

Non-uniform hyperbolicity and non-uniform specification

M

Metric entropy and the number of periodic points

be a compact manifold and

Ergodic properties of invariant measures for C1+a non-uniformly hyperbolic systems

f:,Mrightarrow M

Variational equalities of entropy in nonuniformly hyperbolic systems

be a

The structure on invariant measures of C 1 generic diffeomorphisms

C^1

Non-uniformly hyperbolic periodic points and uniform hyperbolicity for C1 diffeomorphisms

ndiffeomorphism on

Nonexistence of Lyapunov exponents for matrix cocycles

M

Dominated splitting, partial hyperbolicity and positive entropy

. If

Topological pressure for the completely irregular set of birkhoff averages

mu