Recent Publications of HK

I gratefully acknowledge the continued support of the National Science Foundation for my research. My current investigations in the Geosciences is supported by the National Science Foundation grant CMG#0825547.

Heteroclinic connections in fluid exchange:

I. Rypina, M. Brown, and H. Kocak. Transport in an idealized three-gyre system with application to the Adriatic Sea, J. Physical Oceanography , to appear.
Stability of belts and zones of Jupiter:

Beron-Vera, F. J., M. G. Brown, M. J. Olascoaga, I. I. Rypina, H. Kocak and I. A. Udovydchenkov, Zonal jets as transport barriers in planetary atmospheres, , J. Atmos. Sci., to appear.
Run-off as source of harmful algal blooms:

Olascoaga, M. J., F. J. Beron-Vera, L. E. Brand and H. Kocak. Tracing the early development of harmful algal blooms with the aid of Lagrangian coherent structures, J. Geophys. Res., to appear ( http://arxiv.org/abs/0708.4198).
Why degenerate tori are surprisingly stable:

Rypina, I., F. J. Beron-Vera, M. G. Brown, H. Kocak, M. J. Olascoaga, and I. A. Udovydchenkov,. Robust transport barriers resulting from strong Kolmogorov-Arnold-Moser stability, Phys. Rev Lett. 98, 104102 (2007).

Stability of the boundary of the Antarctic ozon hole:

Rypina, I. I., F. J. Beron-Vera, M. G. Brown, H. Kocak, M. J. Olascoaga and I. A. Udovydchenkov, On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Impermeability of the  Stratospheric Polar Vortex, J. Atmos. Sci., 64: 3595-3610.
Forbidden zone on the West Florida Shelf:

Olascoaga, M. J., I. I. Rypina, M. G. Brown, F. J. Beron-Vera, H. Kocak, L. E. Brand, G. R. Halliwell and L. K. Shay, Persistent Transport Barrier on the West Florida Shelf, Geophys. Res. Lett., 33, L22603, doi:10.1029/2006GL027800.
Rigorous Computations in ODEs: A Review

H. Kocak, K. Palmer, and B. Coomes. Shadowing in Ordinary Differential Equations, Rend. Sem. Mat. Univ. Pol. Torino , 65, 89-114 (2007).
Computer-assisted proof of Shilnikov orbits

B. Coomes, H. Kocak, and K. Palmer. Shilnikov saddle-focus Homoclinic Orbits from Numerics: Higher Dimensions, To appear in J. Dynamics and Diferential Equations , to appear (2021).
Computer-assisted proof of connecting orbits in ODEs:

B. Coomes, H. Kocak, K. Palmer. Transversal Connecting Orbits from Shadowing , Numer. Math. , 106, 427-469 (2007).
Computer-assisted proof of connecting orbits in maps:

B. Coomes, H. Kocak, K. Palmer. Homoclinic Shadowing , J. Dynamics and Differential Equations, 17, 175-215 (2005).
Lossless image compression:

B. Koc, Z. Arnavut, D. Sarkar, and H. Kocak. Technique for lossless compression of color images based on hierarchical prediction, inversion, and context adaptive coding, Journal of Electronic Imagings, 28(5), 053007 (1-11) (2019).