We consider a discrete dynamical system on a compact manifold ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn1.gif] {$M$} generated by a homeomorphism ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn2.gif] {$f$} . Let ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn3.gif] {$C=\{M(i)\}$} be a finite covering of ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn1.gif] {$M$} by closed cells. The symbolic image of a dynamical system is a directed graph ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn4.gif] {$G$} with vertices corresponding to cells in which vertices ##IMG## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn5.gif] {$i$} and ##IMG## [http://ej.iop.org/images/1064-5616/211/7/104...] {$j$}

中文翻译：

---

轨迹和不变测度的编码

我们考虑在紧凑流形上的离散动力系统## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn1.gif] {$ M $}由同种异体## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn2.gif] {$ f $}。令## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn3.gif] {$ C = \ {M（i）\} $}为有限元封闭单元格覆盖了## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn1.gif] {$ M $}。动力系统的符号图像是有向图## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn4.gif] {$ G $}，带有顶点对应于其中顶点## IMG ## [http://ej.iop.org/images/1064-5616/211/7/1041/MSB_211_7_1041ieqn5.gif] {$ i $}和## IMG ## [ http：//ej.iop.org/images/1064-5616/211/7/104 ...] {$ j $}