## 6 Conclusions  
In summary, details of the breakup and recombination of the interior as well as the exterior resonant periodic families with the _RTPFs_ are revealed in this work with increasing \(\mu\). Starting from the first-order resonant periodic families in the Sun-Earth system, we gradually increase the mass parameter \(\mu\) to the Sun-Jupiter systems. In the process of continuing these periodic families, we observe the gradual changes in the phase space structure of the first-order resonance due to the increasing perturbation strength from the secondary in the CRTBP model. Two phenomena are reported. (1) With the mass parameter \(\mu\) increasing, the strength of the 1:1 resonance becomes stronger. Starting from large values of \(p\), the interior \((p+1)\):\(p\) and the exterior \(p\):\((p+1)\) resonances are gradually overlapped by the 1:1 resonance, in a way that the characteristic curves of these resonance periodic families break up, recombine, and finally disappear. (2) Resonance transition periodic orbits connecting the 1:1 resonance and the interior/exterior resonances appear, forming the bridge connecting the 1:1 resonance region with the interior/exterior resonances. Their appearance indicates that the resonances are already obviously influenced by the 1:1 resonance. Furthermore, starting from the planar Lyapunov orbits in the 1:1 resonance region, we propose an efficient way to compute the symmetric resonance transition periodic orbits, and some examples are presented for the Sun-Jupiter system. We have to remark that breakup and recombination of interior/exterior resonances with the _RTPFs_ cause difficulties when continuing periodic families from the \(\mu=0\) to large values of \(\mu\), because according to our study, the periodic families may undergo many breakups and recombination events during the continuation process, leading to a phase space (for large values of \(\mu\)) quite different from that of the two-body problem. Some resonance periodic families may even disappear. We also remark that there are still some limitations of the current work. For example, the regularization method is not used in this work when generating the periodic families, which means that the continuation of the periodic families has to be stopped when the orbit in these families has a close encounter with the primaries. Subsequent work should consider the use of regularization methods to give a more comprehensive understanding of the evolution of the _RTPFs_. In addition, the symmetry property is now exploited in the calculation of periodic orbits, and it is worthwhile to further investigate some non-symmetric _RTPFs_, which also have some possible applications for mission designs. Figure 16: Example _RTPOs_ passing through the \(L_{2}\) region in the Sun–Jupiter system. (**a**) Orbit-1: initials generated by the second intersection of the trajectory with the \(x\)-axis (see Figure 14b). (**b**) Orbit-2 and (**c**) Orbit-3: initials generated by the third intersection of the trajectory with the \(x\)-axis (see Figure 14c). (**d**) Orbit-4, (**e**) Orbit-5 and (**f**) Orbit-6: initials generated by the fourth intersection of the trajectory with the \(x\)-axis (see Figure 14d). The larger and the smaller blue dots represent the positions of \(P_{1}\) and \(P_{2}\), respectively. **Author Contributions:** Conceptualization, S.P. and X.H. ; methodology, S.P. and X.H. ; formal analysis, S.P. and X.H. ; investigation, S.P. ; data curation, S.P. ; writing--original draft preparation, S.P. ; writing--review and editing, X.H. ; supervision, X.H. ; funding acquisition, S.P. and X.H. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China (No. 11773017) and the China Scholarship Council (No. 202006190153). **Data Availability Statement:** Not applicable. **Acknowledgments:** The authors thank the reviewers and editors for their comments and suggestions, which have greatly improved the presentation of our work.