Bifurcation of critical periods of a quartic system

For the polynomial system x˙ = ix + xx¯(ax2 + bxx¯ + cx¯ 2 ) the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical periods can bifurcate from any nonlinear center of the system

Bifurcation of critical periods of a quartic system

For the polynomial system x˙ = ix + xx¯(ax2 + bxx¯ + cx¯ 2 ) the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical periods can bifurcate from any nonlinear center of the system

Linearization of two-dimensional systems of ODEs without conditions on small denominators

We study the problem of linearizability for two-dimensional systems of ODEs in a neighborhood of the saddle type singular point with rationally incommensurable eigenvalues. It is shown that if the linearizing transformation is convergent in one of the variables, then it is absolutely convergent

Bifurcation of critical periods of a quartic system

For the polynomial system $\dot x = ix + x \bar x ( a x^2 + b x \bar x + c \bar x^2)$ the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical periods can bifurcate from any nonlinear center of the system

Rapid deep-water renewal in Lake Issyk-Kul (Kyrgyzstan) indicated by transient tracers

Simultaneous profiles of the transient tracers sulfur hexafluoride (SF6), 3H-3He, and the chlorofluorocarbons CFC-11 and CFC-12 were measured in Lake Issyk-Kul, a large, deep lake in Kyrgyzstan. Apparent water ages derived from these measurements suggest rapid mixing, with a deepwater renewal rate > 10% yr21 at 650 m depth. SF6 and 3H-3He ages agree reasonably well, whereas CFC ages are significantly greater. The discrepancy is explained by the nonlinear relationship between tracer age and tracer concentration and by the flattening of the atmospheric growth curves for CFCs. Novel to physical limnology is the application of SF6 dating, which proves to be an excellent tool for the study of mixing in lakes, complementing 3H-3He and CFC dating techniques