NEW YORK — The stock market stabilized Thursday after three days of volatile trading, but tense investors traded cautiously amid continuing uncertainty about the economy in this country and overseas.

        Although investors were hoping that the 317-point plunge blue chips took Wednesday would inspire a rally, they saw little reason to do much buying.

        The Dow Jones Industrial Average advanced 57.82 to close at 10,031.28 after rising more than 100 points early in the session. The Dow fell below 10,000 on Wednesday for the first time in five months and fluctuated above and below that milestone throughout Thursday's dealings.

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        Broader market indicators were mixed. The Nasdaq Composite Index slipped 31.38 to 1940.71 after falling below 2000 Monday for the first time in more than 27 months.

        Wall Street's broadest measure, the Standard & Poor's 500 Index, rose 6.85 to 1173.56. However, the S&P 500 is down almost 25 percent from its closing high of 1527.46, reached a year ago.

        The dive that blue chips took Wednesday was particularly unsettling because such upsets had for months been largely reserved for the Nasdaq. Investors had taken comfort in thinking the slowing economy was hurting mostly the tech sector, leaving the broader market relatively intact.

        “A lot of people were looking at the staple stocks as sort of immune to the bubble popping that happened in the tech stocks. (But) it has carried over to a limited degree” to blue chips, said Richard A. Dickson, technical analyst at Scott & Stringfellow Inc. in Richmond, Va.

        While the market expected the Nasdaq to test the 2000 level, the Dow's falling below 10,000 was “a yellow flag being raised that the rest of the market isn't immune,” Mr. Dickson said.

        Thursday's slim gains followed a positive session in Japan, in which stocks finished up 2.6 percent. Economic instability in Japan, where the government admitted that the country is in a state of deflation, helped send shares skidding in the United States and in Europe Wednesday.

        Most analysts doubt the market here will move substantially higher anytime soon. They say investors still are grappling with fears that earnings and the economy will be weak for the foreseeable future.

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