Chaos in rational systems in the plane containing quadratic terms (Q450387)
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scientific article; zbMATH DE number 6081910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chaos in rational systems in the plane containing quadratic terms |
scientific article; zbMATH DE number 6081910 |
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Chaos in rational systems in the plane containing quadratic terms (English)
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13 September 2012
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chaos
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Li-Yorke
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Marotto
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snap-back repeller
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rational system
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quadratic
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plane
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The chaotic behavior in the sense of Li-Yorke of the system of two difference equations NEWLINE\[NEWLINE Dx = f_1(x,y)\quad,\quad Dy = f_2(x,y) NEWLINE\]NEWLINE where \(Dx_n=x_{n+1}\), \(Dy_n=y_{n+1}\) and NEWLINE\[NEWLINE \displaystyle{f_i(x,y) = {{A_ix^2+B_ixy+C_iy^2+D_ix+E_i+F_i}\over {\alpha_ix^2+\beta_ixy+\gamma_iy^2+\lambda_ix+\mu_iy+\nu_i}}\quad,\quad i=1,2} NEWLINE\]NEWLINE is considered. The results are proved for the case \(F_1=F_2=0\) and then a topological equivalence to the case \(F_1\neq 0\), \(F_2\neq 0\) is pointed out.
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