California authorities say the whereabouts of a fugitive former Los Angeles police officer suspected in three murders remains a mystery as thousands of officers continue to search for the suspect across three states and into Mexico.

"He could be anywhere at this point," said San Bernardino County Sheriff John McMahon as authorities focused on the area surrounding Bear Mountain Ski Resort.

Christopher Jordan Dorner, 33, is considered extremely dangerous and armed with multiple weapons, authorities say. He is accused of killing a college basketball coach and her fiance last weekend, then following through on a vow to kill police by opening fire Wednesday night on three officers, killing one.

Officers executed a search warrant at the house of Dorner's mother, but it wasn't clear what they were hoping to find there.

The search for Dorner, which had extended across California from the U.S.-Mexico border through Nevada, narrowed in on a cold, snowy mountain Thursday night 80 miles east of Los Angeles where Dorner's burned truck was found.

More On This... Manhunt under way for former Los Angeles cop

However, as of early Friday tracks that surrounded the truck and hours of door-to-door searching around Bear Mountain Ski Resort had turned up nothing, and authorities conceded that the whereabouts of Dorner, also a former Naval reservist and onetime college running back, remained a mystery. Authorities said they followed the tracks surrounding the truck and into the woods until the ground became frozen over.

Authorities grounded an air search due to weather conditions Friday, but continued the ground search. Multiple units remain involved, including the use of canine units.

Police say they plan to continue searching the area until their either find him, or find evidence that he has left the mountain area.

Schools in the Bear Valley School District are closed Friday due to the search and weather conditions. Police said they were ready to provide security at each school in the area, but the district decided to close. Officials say snow showers are making the process difficult, but that equipment from neighboring departments are helping them gain access to mountain roads.

"We don't know what he's going to do," said Cindy Bachman, spokeswoman for the San Bernardino County Sheriff's Department, one of many law enforcement agencies whose primary purpose Thursday became finding Dorner. "We know what he's capable of doing. And we need to find him."

The killings appear to be retaliation for Dorner's 2008 termination from the Los Angeles Police Department for making false statements, authorities say. Dorner posted an online manifesto that warned, "I will bring unconventional and asymmetrical warfare to those in LAPD uniform whether on or off duty."

It also asserted: "Unfortunately, I will not be alive to see my name cleared. That's what this is about, my name. A man is nothing without his name."

Los Angeles police believe the manifesto posted to Facebook was written by Dorner because there are details in it only he would know.

"In this case, we're his target," Sgt. Rudy Lopez from the Corona Police Department told reporters Thursday morning after an attack on the department's officers.

Law enforcement officials are also inspecting a package CNN anchor Anderson Cooper apparently received from Dorner at the beginning of the month.

CNN spokeswoman Shimrit Sheetrit said Thursday that a parcel containing a note, a DVD and a bullet hole-riddled memento were sent by Dorner and addressed to Cooper's office.

LAPD Cmdr. Andrew Smith says LAPD robbery-homicide detectives will inspect the package for clues. The package arrived Feb. 1, days before the first two killings Dorner is accused of.

It contained a note on it that read, in part, "I never lied."

Dorner's pickup truck was found burned out near the Big Bear ski area Thursday morning about 80 miles east of Los Angeles. A 10-man tactical team arrived to search the surrounding area. Several Big Bear schools were put on lock-down, and the ski resort closed its slopes, as FBI agents manned a checkpoint to question drivers leaving the area.

A U.S. Marshals Service official says the search for Dorner has expanded from California to Nevada, Arizona and Mexico.

The massive manhunt began after Dorner was linked to a weekend killing, in which one of the victims was the daughter of a former police captain who had represented Dorner during his disciplinary hearing. Authorities think Dorner followed up that attack by opening fire late Wednesday on police in cities east of Los Angeles, killing an officer and wounding another.

"Nobody else needs to die," Los Angeles Police Chief Charlie Beck said urging Dorner to surrender. "Of course he knows what he's doing, we trained him. He was also a member of the armed forces. It is extremely worrisome and scary."

Beck detailed Dorner's alleged crimes in an unusual press conference in an underground room at police headquarters, where extra security was deployed. The chief said there had been a "night of extreme tragedy in the Los Angeles area" and that all measures were being implemented to ensure officer safety.

Dorner served in Iraq, providing security on an oil platform and has received awards including the Rifle Marksman Ribbon and a Pistol Expert Medal, among others. Based on his awards and deployment records, the Navy told FoxNews.com that Dorner would not be classified as an advanced shooter.

Dorner is wanted in the killings of Monica Quan and her fiance, Keith Lawrence. They were found shot in their car at a parking structure at their condominium on Sunday night in Irvine, authorities said. Quan, 28, was an assistant women's basketball coach at Cal State Fullerton. Lawrence, 27, was a public safety officer at the University of Southern California.

Quan's father, a former LAPD captain who became a lawyer in retirement, represented Dorner in front of the Board of Rights, a tribunal that ruled against Dorner at the time of his dismissal.

According to documents from a court of appeals hearing in October 2011, Dorner was fired from the LAPD after he made a complaint against his field training officer, Sgt. Teresa Evans. Dorner said that in the course of an arrest, Evans kicked suspect Christopher Gettler, a schizophrenic with severe dementia.

Richard Gettler, the schizophrenic man's father, gave testimony that supported Dorner's claim. After his son was returned on July 28, 2007, Richard Gettler asked "if he had been in a fight because his face was puffy," and his son responded that he was kicked twice in the chest by a police officer.

The first attack on officers occurred early Thursday in Corona and involved two LAPD officers working a security detail, Los Angeles Sgt. Alex Baez said. A citizen pointed out Dorner to the officers, who followed him until his pickup stopped and he got out, allegedly fired a rifle at them, officials said. One officer's head was grazed by a bullet.

Later, two officers on routine patrol in neighboring Riverside were ambushed at a stoplight by a motorist, suspected to have been Dorner, who drove up next to them and opened fire with a rifle. One died and the other was seriously wounded but was expected to survive, Riverside Police Chief Sergio Diaz said.

Diaz said news organizations should withhold the officers' names because the suspect had made clear that he considers police and their families "fair game."

Dorner's LAPD badge and an ID were found near San Diego's airport and were turned in to police at early Thursday, San Diego police Sgt. Ray Battrick said.

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The Associated Press contributed to this report.