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Article

Properties of the Tent map for decimal fractions with fixed precision

Journal of Physics: Conference Series. 2018. Vol. Volume 955. No. 012025. P. 1-5.

The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if the first term of the recurrence sequence is taken as a decimal fraction with a fixed number "k" of digits after the decimal point and all calculations are carried out accurately, then the situation turns out to be completely different. In this case, first, the Tent map does not lead to an increase in significant digits in the terms of the sequence, and secondly, demonstrates the existence of a finite number of eventually periodic orbits, which are attractors for all other decimal numbers with the number of significant digits not exceeding "k".