Emerald Atlas by John Stephens

In the first of a projected trilogy, orphaned siblings Kate, Michael, and Emma find a book that transports them back in time 15 years. From old familiar fantasy elements, Stephens creates a new story. The children are treated individually, each with a distinct personality. There is bickering, there are rivalries, but all three hide a fierce, underlying loyalty to one another. Every child will identify with at least one of the three siblings. Perhaps this is the next Percy Jackson.