WASHINGTON — The smog that often hangs over Beijing was expected to lift ahead of President Barack Obama’s arrival as the guest of Chinese President Xi Jinping on Monday, but no one is expecting that their three-day visit will really clear the air.

Clashes over cybersecurity, trade, human rights and regional territorial disputes have left relations between the two nations at a pronounced low, creating distrust and rivalry and leaving the leaders struggling to cooperate on a number of goals.

Even the areas where progress might come – possible deals on climate change and military coordination – are likely to yield more show than substance.

But while diplomats are skeptical that Obama and Xi will deliver any groundbreaking agreements, advisers to the president hope the two will take symbolic steps forward.

If they can shake hands on a couple of small deals, said one aide, “That would be progress.”

Obama’s visit, timed so he can participate in the annual Asia-Pacific Economic Cooperation summit, opens a three-leg, weeklong trip that will also take him to Myanmar and the Group of 20 summit in Australia.

His trip follows closely on the heels of midterm elections that were bruising for Obama’s fellow Democrats. Republicans won enough Senate seats to wrest control of Congress.

After a summit with congressional leaders Friday and the nomination of a new attorney general, Obama’s next big move is to beat a departure to a part of the world where he’s likely to find some welcome audiences.

His first stop in Beijing has prompted the Chinese government to take strict anti-pollution measures to curb car use and factory emissions for 10 days, as it memorably did in the run-up to the Beijing Olympics in 2008. Officials have even banned cremation this week to reduce pollution.

Whether Xi and Obama can find common ground on long-term environmental protection steps remains to be seen.

In recent months, China and the U.S. talked about possibly announcing targets for reducing Chinese carbon emissions, and about how American technology might help China reach those goals.

They may also agree on protocols for steering around each other during major military activities and on rules of behavior at sea and in the air.

Although those incremental steps might not bode a new era of peace and harmony, experts say, they are a small step toward progress.

“The point of the meeting is not to deliver very much. The point of the meeting is to have the meeting,” said Steve Tsang, a China expert at Britain’s University of Nottingham.

“If they meet more regularly, they have a better scope for understanding each other and, if they get into really difficult issues, there is a reduced risk of misunderstanding the other,” he said. “That in itself is a good thing.”

Hopes of mutual understanding ran high after an informal meeting between Xi and Obama in Sunnylands, Calif., last year. The two men emerged talking of “a new model of relations between great powers.”

Friction persisted anyway.

Chinese officials object to what they see as a U.S. “containment” strategy against them, as evidenced by an Obama administration plan to boost trade and democracy in Asia – and to position 60 percent of its naval forces in the region by 2020.

Recently, the Xi government accused Washington of butting into domestic concerns including the ongoing democracy protests in Hong Kong, a former British territory that returned to Chinese rule in 1997 to be governed separately from the rest of the country. Protesters in September denounced rules the Chinese government laid out for future elections in Hong Kong.

For its part, the Obama administration is miffed by what it says is Chinese government-directed hacking of American companies.

Such disagreements can effectively impede the two countries’ search for consensus on pressing issues, including their joint effort to get North Korea to give up its nuclear program.

But Xi wants to show a willingness to cooperate and engage with other leaders, enough to soothe fears and quell anti-China sentiment, said Patrick Cronin, senior director of the Asia-Pacific Security Program at the Center for a New American Security.

Environmental policy might present such an opportunity. China has made progress in curbing its dependence on coal. This year marked the first time in decades that its coal consumption decreased.

The Chinese vice premier signaled at a fall climate summit in New York that China would make its economy much more carbon-efficient by 2020.

It was a rare public promise to act, but Xi wasn’t present at the summit to make it. Now, aides to Obama wonder whether Xi is willing to embrace the idea personally.

The coming 10 days will be full of such delicate dances of diplomacy as Obama attends major summits in three countries.

While meeting with East Asian leaders in Myanmar, Obama plans to address smaller countries’ security concerns about the rise of China. At the same time, he’ll try to shine a light on the democratic reforms in the once-cloistered country while also urging leaders to improve their record on human rights.

The Myanmar government has done little to protect the persecuted Rohingya people, demanding that they prove their families have lived in the country for several decades or face deportation.

Later, on the sidelines of the G-20 summit in Australia, Obama may have an informal chat with Russian President Vladimir Putin, the first such conversation in months. Last spring, the members of the Group of 8 leading industrialized nations voted to suspend Russia in response to Russia’s annexation of Crimea.

The two leaders will not have formal talks with each other, but they have an interest in keeping diplomatic channels open. Because of its strong relations with Syria and Iran, Russia is a potential player in several contentious conflicts.

Likewise, despite disagreement over their military presences in the Asia Pacific, the U.S. and China may begin to tiptoe toward each other on the subject of military relations.

The two sides are working on an update to the rules of notification for major military activities and rules of behavior at sea and in the air.

The talks took on more urgency in August, after Pentagon officials said a Chinese fighter jet had engaged in an “aggressive” and “dangerous” move to intercept a U.S. Navy sub-hunter aircraft.

Beijing said the maneuver was a legitimate response to “large-scale and highly frequent close-in reconnaissance” by American aircraft.

Analysts say an agreement on a code of conduct could prevent such misunderstanding, and perhaps some near misses, in the future.

“That would represent a commitment by both sides to try and avoid any accidents and potential escalation,” said Bonnie Glaser, Asia specialist at the Center for Strategic and International Studies. “And it would represent what is a change of thinking in Beijing, and President Xi’s recognition about how dangerous these things can be.”

Ultimately, though, a handshake between the two leaders isn’t what matters, said Glaser.

On any agreement they craft, she said, the implementation is what will give them meaning. For that reason, she said, their apparent movement toward agreement may be symbolically significant.