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Consider a closed coisotropic submanifold $N$ of a symplectic manifold$(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result ofthis article states that $\phi$ has at least the cup-length of $N$ manyleafwise fixed points w.r.t. $N$, provided that it is the time-1-map of aglobal Hamiltonian flow whose restriction to $N$ stays $C^0$-close to theinclusion $N\to M$. If $(\phi,N)$ is suitably nondegenerate then the number ofthese points is bounded below by the sum of the Betti-numbers of $N$. Thenondegeneracy condition is generically satisfied.  This appears to be the first leafwise fixed point result in which neither$\phi\big|_N$ is assumed to be $C^1$-close to the inclusion $N\to M$, nor $N$to be of contact type or regular (i.e., "fibering"). It is optimal in the sensethat the $C^0$-condition on $\phi$ cannot be replaced by the assumption that$\phi$ is Hofer-small.

Leafwise fixed points for $C^0$-small Hamiltonian flows