## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

JMD

We prove that typical area-preserving flows with linearly isomorphic nondegenerate saddles on genus two surfaces are not mixing.

JMD

We prove that for any $\epsilon>0$ the growth rate $P_n$
of generalized diagonals or periodic orbits of a typical (in the
Lebesgue measure sense) triangular billiard satisfies:
$P_n < Ce^{n^{\sqrt{3}-1+\epsilon}}$. This provides an explicit subexponential estimate on the triangular billiard complexity and
answers a long-standing open question for typical triangles. This
also makes progress towards a solution of Problem 3 in Katok's list
of "Five most resistant problems in dynamics". The proof uses
essentially new geometric ideas and does not rely on the rational
approximations.

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