Given 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 -principle. The flexibility follows from the -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 -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.

中文翻译：

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接触结构横向嵌入的 h 原理

给定一类嵌入到接触或辛流形中的向量，我们给出一个充分条件，我们称之为等接触或等辛实现，以使该类满足一般条件-原则。灵活性来自于-等接触和等辛嵌入的原理，它为经典结果提供了框架，并且我们给出了两个新的应用。我们的主要结果是横向于接触结构的嵌入满足完全-两种情况下的原理：如果嵌入的补集被过度扭曲，或者当形式导数的图像与接触结构的交集严格包含在真辛子丛中时。我们通过一类嵌入研究常规水平集上哈密顿动力学的普遍性，说明了辛流形的一般框架。