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Vamos utilizar a fun\[CCedilla]\[ATilde]o que definimos para estimar os \
expoentes de Lyapunov dos casos de dois slides atr\[AAcute]s:\
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\[UAcute]mero de aplica\[CCedilla]\[OTilde]es do mapa \[EAcute] bem \
r\[AAcute]pida. O resultado negativo \[EAcute] compat\[IAcute]vel com o que \
observamos antes."
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\[CCedilla]\[OTilde]es:"
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Vemos que a converg\[EHat]ncia lenta se mant\[EAcute]m, mas parece seguro \
supor que com 10000 itera\[CCedilla]\[OTilde]es temos uma precis\[ATilde]o de \
dois algarismos significativos no c\[AAcute]lculo do expoente.\
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Finalmente produzimos o gr\[AAcute]fico do expoente de Lyapunov do mapa log\
\[IAcute]stico em fun\[CCedilla]\[ATilde]o do par\[AHat]metro \[Lambda]:\
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\[CCedilla]\[ATilde]o de per\[IAcute]odo e \[EAcute] positivo, assinalando \
comportamento ca\[OAcute]tico, em quase todos os pontos na faixa acima de ",
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de atratores correspondentes a ciclos finitos, como hav\[IAcute]amos visto \
nos diagramas de bifurca\[CCedilla]\[ATilde]o. (A fun\[CCedilla]\[ATilde]o \
Timing retorna o tempo de computador, em segundos, utilizado para executar \
uma instru\[CCedilla]\[ATilde]o. Em processadores com v\[AAcute]rios n\
\[UAcute]cleos, o tempo indicado pode n\[ATilde]o corresponder ao tempo \
decorrido no \[OpenCurlyDoubleQuote]mundo real\[CloseCurlyDoubleQuote].)"
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na regi\[ATilde]o majoritariamente ca\[OAcute]tica, mas para acelerarmos o c\
\[AAcute]lculo precisamos compilar a fun\[CCedilla]\[ATilde]o que estima o \
expoente, ou seja, precisamos transform\[AAcute]-la em \
\[OpenCurlyDoubleQuote]c\[OAcute]digo de m\[AAcute]quina\
\[CloseCurlyDoubleQuote]. Isso pode ser feito com o uso de ",
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sejam incorporadas ao c\[OAcute]digo, o que faremos com o aux\[IAcute]lio de \
uma fun\[CCedilla]\[ATilde]o pura e da forma expl\[IAcute]cita da derivada. A \
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Note que o tempo necess\[AAcute]rio para produzir o gr\[AAcute]fico \
reduziu-se em mais de uma ordem de magnitude. Compilar \
fun\[CCedilla]\[OTilde]es requer um conhecimento mais t\[EAcute]cnico de \
computa\[CCedilla]\[ATilde]o e as fun\[CCedilla]\[OTilde]es compiladas sup\
\[OTilde]em valores num\[EAcute]ricos dos argumentos. Utilizar valores simb\
\[OAcute]licos implica ignorar a compila\[CCedilla]\[ATilde]o, ou seja, o \
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forma padr\[ATilde]o.\
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E ampliando a regi\[ATilde]o em que regime passa de regular para \
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Essas amplia\[CCedilla]\[OTilde]es evidenciam a exist\[EHat]ncia das \
\[OpenCurlyDoubleQuote]ilhas de estabilidade\[CloseCurlyDoubleQuote], com \
expoente negativo, mesmo nas regi\[OTilde]es em que o comportamento \[EAcute] \
majoritariamente ca\[OAcute]tico, ou seja, com expoente positivo. Essas ilhas \
existem em todas as escalas, mais uma manifesta\[CCedilla]\[ATilde]o de \
comportamento fractal.\
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Cell["O mapa de H\[EAcute]non", "Section",
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 "Vamos agora considerar o mapa bidimensional de H\[EAcute]non, definido \
pelas equa\[CCedilla]\[OTilde]es recursivas\[LineSeparator]",
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Cell[TextData[{
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 "O mapa de H\[EAcute]non tamb\[EAcute]m leva a comportamentos \
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O que se observa nesse caso \[EAcute] um \[OpenCurlyDoubleQuote]atrator \
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Esse tipo de atrator indica que n\[ATilde]o h\[AAcute] uma periodicidade nos \
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Agora criamos a fun\[CCedilla]\[ATilde]o que produz o gr\[AAcute]fico \
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