  A famous result by R\"odl, Ruci\'nski, and Szemer\'edi guarantees a (tight)
Hamilton cycle in $k$-uniform hypergraphs $H$ on $n$ vertices with minimum
$(k-1)$-degree $\delta_{k-1}(H)\geq (1/2+o(1))n$, thereby extending Dirac's
result from graphs to hypergraphs. For graphs, much more is known; each graph
on $n$ vertices with $\delta(G)\geq (1/2+o(1))n$ contains $(1-o(1))r$
edge-disjoint Hamilton cycles where $r$ is the largest integer such that $G$
contains a spanning $2r$-regular subgraph, which is clearly asymptotically
optimal. This was proved by Ferber, Krivelevich, and Sudakov answering a
question raised by K\"uhn, Lapinskas, and Osthus.
  We extend this result to hypergraphs; every $k$-uniform hypergraph $H$ on $n$
vertices with $\delta_{k-1}(H)\geq (1/2+o(1))n$ contains $(1-o(1))r$
edge-disjoint (tight) Hamilton cycles where $r$ is the largest integer such
that $H$ contains a spanning subgraph with each vertex belonging to $kr$ edges.
In particular, this yields an asymptotic solution to a question of Glock,
K\"uhn, and Osthus.
  In fact, our main result applies to approximately vertex-regular $k$-uniform
hypergraphs with a weak quasirandom property and provides approximate
decompositions into cycle factors without too short cycles.
