Description
![](../../doubling/t1.gif)
1D maps
The period-doubling accumulation point in unimodal map of 4-th power.
For bimodal 1D maps - the limit of period-doubling on a special curve
in the parameter plane defined by the condition "extremum is mapped to
extremum". T-point appears as the terminal point of the Feigenbaum curve. This type of critical behavior is known after Chang, Wortis, Wright, and Fraser and Kapral.
More general systems
T-point may appear generically only in codimension 3. In some cases the
pseudo-tricritical behavior may occur, as an intermediate asymptotics.
RG equation
![](../../doubling/t2.gif)
The fixed point
![](../../doubling/t3.gif)
The orbital scaling factor
![](../../doubling/t4.gif)
Critical multiplier
![](../../doubling/t5.gif)
Relevant eigenvalues
![](../../doubling/t6.gif)
Codimension
CoDim=3 (restr. 2)
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Codimension-2 example
![](../../doubling/t7.gif)
![](../../doubling/t8.gif)
Param. space arrangement and scaling with factors
![](../../doubling/t9.gif)
Scaling coordinates
![](../../doubling/t11.gif)
![](../../doubling/t10.gif)
show enlarged figure
Codimension-3 example
,
tricritical point at
![](../../doubling/t13.gif)
Codimension-3 example in 2D invertible map
.
For D=0.3 the tricritical point is located at
![](../../doubling/t15.gif)
![](../../doubling/t16.gif)
show enlarged figure
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