Cardona Aguilar, RobertPresas Mata, Francisco2025-03-042025-03-102024-03-111753-8416https://hdl.handle.net/2445/219434Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general $h$-principle. The flexibility follows from the $h$-principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full $h$-principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.33 p.application/pdfeng(c) London Mathematical Society, 2024Varietats topològiquesTopologia diferencialTopological manifoldsDifferential topologyinfo:eu-repo/semantics/article7459052025-03-04info:eu-repo/semantics/openAccess