Resonance Identities for Closed Characteristics on Compact Star-shaped Hypersurfaces in R2n{\bf R}^{2n}

Resonance relations among periodic orbits on given energy hypersurfaces are very important for getting deeper understanding of the dynamics of the corresponding Hamiltonian systems. In this paper, we establish two new resonance identities for closed characteristics on every compact star-shaped hypersurface $\Sigma$ in ${\bf R}^{2n}$ when the number of geometrically distinct closed characteristics on $\Sigma$ is finite, which extend those identities established by C. Viterbo in 1989 for star-shaped hypersurfaces assuming in addition that all the closed characteristics and their iterates are non-degenerate, and that by W. Wang, X. Hu and Y. Long in 2007 for strictly convex hypersurfaces in ${\bf R}^{2n}$.Comment: arXiv admin note: substantial text overlap with arXiv:math/0701608. To appear in Journal of Functional Analysis, this is the final versio

KS0−KL0K_S^0-K_L^0 Asymmetries and CPCP Violation in Charmed Baryon Decays into Neutral Kaons

We study the $K^0_S-K^0_L$ asymmetries and $CP$ violations in charm-baryon decays with neutral kaons in the final state. The $K^0_S-K^0_L$ asymmetry can be used to search for two-body doubly Cabibbo-suppressed amplitudes of charm-baryon decays, with the one in $\Lambda^+_c\to pK^0_{S,L}$ as a promising observable. Besides, it is studied for a new $CP$-violation effect in these processes, induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the neutral kaon mixing. Once the new CP-violation effect is determined by experiments, the direct $CP$ asymmetry in neutral kaon modes can then be extracted and used to search for new physics. The numerical results based on $SU(3)$ symmetry will be tested by the experiments in the future.Comment: 15 pages, 3 tables. Version published in JHE