What is an example of a compact manifold which do not admit a diffeomorphism with at least one dense orbit?

Moreover, is it true to say that every isometry of $\mathbb{C}P^n$ with the Fubbini Study metric do not posses any dense orbit?

What is an example of a compact manifold which does not admit a diffeomorphism with at least one dense orbit?

Moreover, is it true to say that every isometry of $\mathbb{C}P^n$ with the Fubini-Study metric do not possess any dense orbit?

What is an example of a compact manifold which do not admit a diffeomorphism with at least one dense orbit?

What is an example of a compact manifold which do not admit a diffeomorphism with at least one dense orbit?

Moreover, is it true to say that every isometry of $\mathbb{C}P^n$ with the Fubbini Study metric do not posses any dense orbit?