论文标题
一类本质上横向螺线管吸引子在高尺寸的维度
Dimension of a class of intrinsically transversal solenoidal attractors in high dimensions
论文作者
论文摘要
We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is sufficiently strong, the expansion is close to conformal and the attractor satisfy a geometrical condition of transversality between its components, then the Hausdorff and box-counting dimension of every stable section of the attractor have the same value, which corresponds to the zero of the topological pressure as in Bowen's 公式。我们还计算了吸引子的维度，并证明它在此类中是连续的。
We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is sufficiently strong, the expansion is close to conformal and the attractor satisfy a geometrical condition of transversality between its components, then the Hausdorff and box-counting dimension of every stable section of the attractor have the same value, which corresponds to the zero of the topological pressure as in Bowen's formula. We also calculate the dimension of the attractor and prove that it is continuous in this class.
