Dic: under (some of its usages reviewed)

■■ Collins 4 △subject to the supervision, jurisdiction, control, or influence of
  ■ OALD 4 △used to say who or what controls, governs, or manages someone or something
  ■ COBUILD 8 △If something happens under a particular person or government, it happens when that person or government is in power.

• The country is now under martial law. 
• The coinage was reformed under Elizabeth I (= when she was queen).
• She has a staff of 19 working under her.
• Under its new conductor, the orchestra has established an international reputation.
• There would be no new taxes under his leadership.
• ...the realities of life under a brutal dictatorship...

  ■ OALD 5 △according to an agreement, a law or a system
  ■ COBUILD 7 △If something happens under a law, agreement, or system, it happens because that law, agreement, or system says that it should happen.

• Six suspects are being held under the Computer Fraud and Abuse Act.
• Under the terms of the lease you had no right to sublet the property.
• Is the television still under guarantee?
• Under law, your employer has the right to hire a temporary worker to replace you...
• Under the Constitution, you cannot be tried twice for the same crime.

■■ COLLINS 5 △subject to (conditions); in (certain circumstances)
  ■ OALD 7 △affected by something
  ■ OALD 6 △experiencing a particular process
  ■ COBUILD 5 △You can use under before a noun to indicate that a person or thing is being affected by something or is going through a particular process.

• The wall collapsed under the strain.
• I've been feeling under stress lately.
• I'm under no illusions about what hard work this will be.
• You'll be under anesthetic, so you won't feel a thing.
• The hotel is still under construction.
• The matter is under investigation.
• ...fishermen whose livelihoods are under threat...
• I'm rarely under pressure and my co-workers are always nice to me...
• Firemen said they had the blaze under control...
• He was rushed to court yesterday under armed guard.

CF. COLLINS 9 △powered by: under sail

.... COLLINS, OALD, COBUILD