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A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that thesingularity in generic gravitational collapse is locally oscillatory is testednumerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \timesR$. If the velocity term dominated (VTD) solution to Einstein's equations issubstituted into the Hamiltonian for the full Einstein evolution equations, oneterm is found to grow exponentially. This generates a prediction thatoscillatory behavior involving this term and another (which the VTD solutioncauses to decay exponentially) should be observed in the approach to thesingularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution  versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to  ftp://vela.acs.oakland.edu/pub/berger/u1genfig

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>×</mml:mo><mml:mi>R</mml:mi></mml:math>

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies onT3×R