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The specific implementation of the dominant_cycle function needs to be done using ta.ht_dominant_cycle_period or by calculating the rate of change of the phase, which requires detailed technical processing in actual coding.
How to use the "Market Mathieu Oscillator":
• Green background (stable zone): The market is likely to be in a consolidation or mean reversion state. Trend strategies are riskier, while range trading or option seller strategies may be more dominant.
• Yellow background (warning zone): The market has entered a "flammable" state where resonance may occur. Counter-trend trading should be reduced, and preparations for potential breakthroughs should be started, tightening stops.
• Red background (unstable/resonance zone): **Highest alert! ** This shows that the market is not only "flammable", but also has a "spark" (strong driving force). This is the stage where the trend is most likely to accelerate and sustain itself. Counter-trend operations should be strictly avoided, and trend-following strategies should be actively adopted.
• Q Oscillator:
• The rising q value means that emotions are moving to extremes and the "fuel" of the trend is increasing.
• The q-value is falling, indicating that sentiment is returning to neutrality and the "fuel" of the trend is decreasing, which may indicate the exhaustion of the trend or the beginning of consolidation.
• When the q-value exceeds the red threshold line, it indicates that the driving force is extremely strong, which is one of the necessary conditions for entering the red background.

The "Market Mathieu Oscillator" is an innovative attempt to transform a profound physical and financial theory into an intuitive decision-making aid available on TradingView through a proxy and simplified approach. It cannot make precise quantitative predictions like theoretical models, but it provides a whole new dimension to observe the market: it no longer focuses solely on the price itself, but on the relationship between the "force" that drives the price and the "rhythm" of the market itself. Through this lens, traders can better understand when the market may turn from stability to turbulence, and make more strategic decisions.