Now Comes the PIckleball Invasion.

It started with just a few American retirees. These days, two dozen players fill the courts at the municipal sports center most mornings, swinging paddles at plastic balls. There are so many clubs in Mexico dedicated to the U.S. sport that a tournament was held here last year.

“It was a madhouse,” said Victor Guzmán, a 67-year-old entrepreneur from Charlotte who helped pull the event together. President Donald Trump regularly assails the flow of migrants crossing the Mexican border into the United States. Less noticed has been the surge of people heading in the opposite direction. Mexico’s statistics institute estimated this month that the U.S.-born population in this country has reached 799,000 — a roughly fourfold increase since 1990. And that is probably an undercount.

The U.S. Embassy in Mexico City estimates the real number at 1.5 million or more.  They’re a mixed group. They’re digital natives who can work just as easily from Puerto Vallarta as Palo Alto. They’re U.S.-born kids — nearly 600,000 of them — who’ve returned with their Mexican-born parents. And they’re retirees like Guzmán, who settled in this city five years ago and is now basically the pickleball king of San Miguel.

Thousands of Mexicans are moving home are taken into account, the flow of migrants from the United States to Mexico is probably larger than the flow of Mexicans to the United States. The American immigrants are pouring money into local economies, renovating historic homes and changing the dynamics of Mexican classrooms.

“It’s beginning to become a very important cultural phenomenon,” Marcelo Ebrard, Mexico’s foreign minister, said in an interview. “Like the Mexican community in the United States.” And yet, he said, Mexican authorities know little about the size or needs of their largest immigrant group. He has been tasked by President Andrés Manuel López Obrador with changing that.

While the United States is deeply divided over immigration, American immigrants here have largely been welcomed. In San Miguel — where about 10% of the city’s 100,000 residents are U.S. citizens — Mayor Luis Alberto Villareal delivers his annual State of the Municipality address in English and Spanish.

Thanksgiving is celebrated a few weeks after Mexico’s Day of the Dead. Restaurants have adopted “American timing” — serving dinner at the ungodly hour of 6 p.m. — the mayor reports. “Despite the fact that Donald Trump insults my country every day, here we receive the entire international community, beginning with Americans, with open arms and hearts,”

Villareal said. Mexican authorities say that many of the Americans are probably undocumented — typically, they’ve overstayed their six-month visas. But the government has shown little concern. “We have never pressured them to have their documents in order,” Ebrard said. Typically, violators pay a small fine.

Villereal shrugged. “We like people who come to work and help the economy of the city — like Mexicans do in the United States.”

San Miguel de Allende is about 170 miles northwest of Mexico City on a mile-high plateau where the sunshine coaxes bougainvillea to erupt in blazing colors and spill over walls.

U.S. veterans began moving here after World War II to study at the local art institute on the GI Bill. Over the past 30 years, expatriates flooded in, enchanted by the city’s hilly cobblestone streets, soaring Gothic church, and houses painted in sunset colors: dusky rose, peach, yellow, orange.

The scenery isn’t the only draw.

Given the dollar’s strength against the Mexican peso, even an American getting by on Social Security and a modest pension can rent a high-ceilinged apartment, hire a maid and eat out most nights. “You can live here on $2,000 or $3,000 a month — and live well,” Guzmán said.

Technology has shrunk the distance between the countries. In the 1980s, expat author Tony Cohan would contact his daughter in New York by trekking to the “larga distancia” office, where an operator would put a call through, as he recounted in his popular memoir “On Mexican Time.”

These days, Bill Slusser, 66, from Los Angeles, does part-time marketing work for American clients without leaving his home here: “The internet allows that to happen.”