Regardless of how Putin manages to get Trump to behave so submissively, he does, and this brings me to the subject of power. Nominally, I study this. I am a professor of political science. Screw the capitalizations because, whatever. To the degree that politics can be constrained in intellectual terms, it would be the study of power. Who has it, how do they get it, how do they exercise it, etc.? Harold Laswell simply defined politics as: who gets what, when and how? That's more concise, and distributional, but fundamentally, politics are about power.
So, what's power? We now play the definitional game of infinite regress. The ability to control or influence outcomes, right? So, how much influence does Vladimir Putin have over American politics, and what does that say about "power?" We are now into some fuzzy questions about politics that aren't my normal territory, but the fuzziness of the question is directly associated with the ambiguity of the relationship between Trump and Putin.
In normal times, we would say that the President of the United States is clearly the most "powerful" person in the world. His control over military resources, capacity to make appointments and so forth, give him more direct power to influence outcomes than any other single person on the planet. Normally. Throughout history, the relative power of Congress and the Presidency have gone back and forth (see, for example, James Sundquist, although I can't believe I find myself referencing him), although as a single person, the institutional powers of the Presidency give the holder of that office powers, particularly now (go away, Sundquist!), that are going to be difficult to rival. Who, though, can influence a president? Advisors, in normal times. We find ourselves, though, facing at least the possibility of "kompromat," or perhaps just a President whose hero-worship of an autocratic dictator leaves his judgment so blinkered that he cannot make sound decisions (not that he could otherwise anyway).
What, then, could Putin do? That's the question, isn't it? I have already stated my assessment that NATO is no longer a truly functioning treaty organization because Trump would never back NATO over Putin. That gives Putin the capacity to act against NATO, but will he? That's a separate question, and if he doesn't act against NATO, does that... power (?) mean anything? What else can Putin do? We have already seen Trump hand national security secrets over to Russia, getting nothing in return, and I would put a high likelihood on more of that, which is a hell of a lot of power. In many ways, though, Trump is constrained, by Congress, by the rest of the world... Putin can't tell Trump to bomb the shit out of Chechnya to make that problem go away for him. He can't tell Trump to hand over a $100 billion for nothin'. Russia is not a wealthy country. It has nukes, but we aren't the only ones with nukes to check their nuclear capacity. It has a large army, but empire-building in an economically interconnected world has its own risks and problems, which leaves the basic question of what Putin could do, and what he could get from Trump.
This is a difficult question. Putin has power over Trump. Even if all you knew was what you saw yesterday, combined with Trump's penchant for playing social dominance games, you would know that Putin has the upper hand on Trump. What actual power does that give him? Thinking this through, I'm not sure. We have already seen Trump hand over national security secrets. In the open. What else? I don't know, but there's that. Such is the ambiguous nature of power.