dominate the secular dynamics (εGR ∼πPsec/Pout ≫1, so ZLK cycles are fully suppressed).

By contrast, our jumps are purely conservative — the inner semimajor axis is fixed and no dissipation enters — and our SRFs have εi ≪1, so ZLK cycles operate.

While our systems do reach very fast precession rates that become commensurate with the outer orbital period, they do so only transiently during a singly-averaged fluctuation at high e, and for the rest of their evolution the apsidal precession is much slower than the outer orbital frequency.

The ‘resonance’ condition in our case is satisfied far too briefly for Kuntz (2022)’s adiabatic capture mechanism to operate.

We studied only the test-particle quadrupole version of ZLK dynamics in this paper, purely for simplicity — to exhibit nonadiabatic jumps in the cleanest possible setting.

Relaxing any of these assumptions will only make the dynamics more extreme.

At octupole order, for instance, a nonzero outer eccentricity combined with unequal inner masses can drive secular evolution of jz even at the DA level (Katz et al. 2011; Lithwick & Naoz 2011; Naoz 2016; Klein & Katz 2024b).

This evolution is strongly controlled by the sign and value of CK: librating trajectories (CK < 0) undergo little or no secular jz evolution, whereas for rotating ones (CK > 0) it can be highly efficient (Katz et al. 2011; Klein & Katz 2024b).

Since nonadiabatic jumps can flip the sign of CK, they can naturally trigger or quench this octupolar transport.

The interplay between nonadiabatic jumps and octupole-order ZLK dynamics is therefore a natural extension of this study, which we pursue in a companion paper (Klein & Hamilton 2026).

Similarly, there might be some non-trivial interplay between nonadiabatic jumps discussed here and the very long-term modulation of ZLK cycles due to an accumulation of SA terms that is encapsulated in the Brown Hamiltonian (Tremaine 2023).

Finally, we showed some of the consequences of nonadiabatic jumps in this paper but we did not study in detail their causes.

Some progress was made along these 14 Klein & Hamilton lines by HR24 (with GR as the only SRF), but there is much more to do.

In particular it appears from numerical experiments that the microscopic details of the jump behavior and conditions do depend on the SRF in question.

Also we did not develop any theory capable of predicting the jumps’ statistics.

Since very longterm behavior is extremely sensitive to tiny changes in choices of initial phases, the exact approximations used, etc. (see Appendix B) in the end it may only be a statistical description that is most physically meaningful.

We defer a careful study to future work.
of Figure 1 — can undergo nonadiabatic jumps in their approximate ‘invariant’ labels jz and CK.
• These jumps can lead to much more rapid exploration of phase space, including more extreme eccentricity behavior, than would otherwise be expected.

They also provide — to our knowledge — the only known quadrupole-order, three-body mechanism that drives a net, long-term evolution of the angular-momentum component jz.
• No known semi-analytic/modified-DA theory is capable of usefully predicting this behavior.

Only numerical integration of the SA or N-Body equations of motion can be trusted.
5.

SUMMARY
• These effects may have significant astrophysical consequences.

For instance, time spent above a particular eccentricity T(> e) can be orders of magnitude different in the presence of nonadiabatic jumps.

Various population synthesis calculations may need to be revisited in light of this fact.

In this paper we have studied the classic problem of hierarchical triple dynamics in the test-particle quadrupole limit.

In particular, we studied the resulting von Zeipel-Lidov-Kozai (ZLK) oscillations in the singleaveraged (SA) approximation, including precession due to short-range forces (SRFs).

Our key findings can be summarized as follows.

In a companion paper we show how ZLK cycles subject to nonadiabatic jumps become even more extreme when octupolar effects are important.
• Systems that break the double averaging (DA) approximation (so the validity criterion (17) is violated) and are subject to apsidal precession from SRFs — i.e., those sitting in the fourth quadrant
C.H. was partly supported by the John N.

Bahcall Fellowship Fund at the Institute for Advanced Study.

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