[BroJoeK]

Castlebar: "The British approachd Tecumseh (not the other way around) in 1811 with offers of military aid, weapons, support, etc. to keep the U.S. off balance in the Northwest Territory, in an effort to reverse the verdict of the 1783 Treaty of Paris.
If that doesn't meet your definition of an invasion so be it."

The US 1812 declaration of war on Great Britain does not include any reasons, but historians list them as:

• "Trade restrictions brought about by Britain's ongoing war with France,
• The impressment of American merchant sailors into the Royal Navy,
• British support of American Indian tribes against American expansion,
• Outrage over insults to national honour after humiliations on the high seas, and
• Possible American desire to annex Canada."

Since Americans began the war by invading Canada, the word "possible" above is ludicrous.
The correct word is "certainly".

And I would not call British arms supplies to American Indians an "invasion" -- except if you think that somehow those Indians "invaded" the United States!

[Castlebar]

The reasons were outlined in James Madison's letter to congress; the declaration was the answer form Congress.

No where in the Madison Letter, or in the transcripts of congressional debate on te declaration, is there any stated war aim abut annexing all or part of Canada. Private citizens in various roles stated desires along those lines, but the idea that the U.S. went to war to seize Canada has more to do with the anglophile bias of historians and professors that with reality.