Math and theoretical physics articles are full of bold and italics or emphasis.
Personally this makes me feel like I'm now being shouted at with words I still don't understand: It's extremely distracting and doesn't help. For example this isn't made easier by bold and italics, and it's now all I can look at:
In finite dimensions, if the phase spaceissymplectic (i.e., the center of the Poisson algebra consists only of constants), then it must have even dimension , and the maximal number of independent Poisson commuting invariants (including the Hamiltonian itself) is . The leaves of the foliation are totally isotropic with respect to the symplectic form and such a maximal isotropic foliation is called Lagrangian. All autonomous Hamiltonian systems (i.e. those for which the Hamiltonian and Poisson brackets are not explicitly time dependent) have at least one invariant; namely, the Hamiltonian itself, whose value along the flow is the energy. If the energy level sets are compact, the leaves of the Lagrangian foliation are tori, and the natural linear coordinates on these are called "angle" variables. The cycles of the canonical -form are called the action variables, and the resulting canonical coordinates are called action-angle variables (see below).
Manual of style says bold is to be reserved for titles and synonyms. Bolding other keywords thus adds additional potential for confusing, as I try to figure out whether these other entities could be identified with the article topic. For example, in the next paragraph which concepts really should be bolded as alternative article titles for the Integrable systems article? Clearly not superintegrability, which has its own article, but are the others best explained here?
There is also a distinction between complete integrability, in the Liouville sense, and partial integrability, as well as a notion of superintegrability and maximal superintegrability. Essentially, these distinctions correspond to the dimensions of the leaves of the foliation. When the number of independent Poisson commuting invariants is less than maximal (but, in the case of autonomous systems, more than one), we say the system is partially integrable. When there exist further functionally independent invariants, beyond the maximal number that can be Poisson commuting, and hence the dimension of the leaves of the invariant foliation is less than n, we say the system is superintegrable. If there is a regular foliation with one-dimensional leaves (curves), this is called maximally superintegrable.
Italics are preferred for emphasis, but are to be used sparingly (MOS:ITMOS:NOBOLD).
I may be wrong and missing some math-specific style consensus, but I'll be blanket removing excessive bold and italics until I learn otherwise.
, and the maximal number of independent Poisson commuting invariants (including the Hamiltonian itself) is
. The leaves of the foliation are totally isotropic with respect to the symplectic form and such a maximal isotropic foliation is called Lagrangian. All autonomous Hamiltonian systems (i.e. those for which the Hamiltonian and Poisson brackets are not explicitly time dependent) have at least one invariant; namely, the Hamiltonian itself, whose value along the flow is the energy. If the energy level sets are compact, the leaves of the Lagrangian foliation are tori, and the natural linear coordinates on these are called "angle" variables. The cycles of the canonical
-form are called the action variables, and the resulting canonical coordinates are called action-angle variables (see below).
