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**Physics Note****Published**

# **The Gap Road to Chaos and its Main Characteristics**

**M. C. S. Vieira; C. Tsallis**

1988

[**Download PDF **0.5 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb737/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=The%20Gap%20Road%20to%20Chaos%20and%20its%20Main%20Characteristics)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>M. C. S. Vieira; C. Tsallis</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>1988</dd>

<dt>Description</dt>
<dd>We study numerically the three types of asymmetry associated with the map &lt;math&gt;x'=1-\varepsilon_i-a_i|x|^zi&lt;/math&gt; &lt;math&gt;(\,\!&lt;/math&gt;i=1,2 respectively correspond to &lt;math&gt;x&gt;0\,\!&lt;/math&gt; and &lt;math&gt;x\leqq0)\,\!&lt;/math&gt;. The first case is the amplitude asymmetry &lt;math&gt;(a_1 \ne a_2)&lt;/math&gt;, the second case is the exponent asymmetry &lt;math&gt;(z_1 \ne z_2)&lt;/math&gt; and the last one is a discontinuous map &lt;math&gt;(\varepsilon_1 \ne \varepsilon_2) &lt;/math&gt;. In the last case the road to chaos is complete ly new ("gap road"). Chaos now is attained through sequences of inverse cascades. Various new features are observed, concerning the phase diagram, kneading sequences, Liapunov and uncertainty exponents, number of attractors, multifractality, among others. We also study the crossover between the discontinuous map and the continuous one.</dd>

<dt>Year</dt>
<dd>1988</dd>

<dt>Number</dt>
<dd>CBPF-NF-028/88</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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