存心 发表于 2025-3-27 00:49:45
Maren Zschache measures reflect the asymptotic “shape” of a sequence of high frequency eigenmodes. The quantum ergodicity theorem states that the vast majority of the eigenstates is associated with the “flat” (Liouville) measure. A major open problem addresses the existence of “exceptional” eigenmodes admitting幻想 发表于 2025-3-27 05:03:31
onal with coordinates . and . or . and ., as in the common Newtonian notation. If instead we were dealing with a cloud of . particles, each of mass ., the phase space would be 2.-dimensional with coordinates .., ..,..., .., .., .., ..., ... Note that . indicates the number of independent positions oA精确的 发表于 2025-3-27 06:25:42
Maren Zschach be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-978-1-4613-6482-5978-1-4615-3360-3Metastasis 发表于 2025-3-27 13:04:39
http://reply.papertrans.cn/47/4611/461027/461027_34.png项目 发表于 2025-3-27 15:32:26
Maren Zschachonal with coordinates . and . or . and ., as in the common Newtonian notation. If instead we were dealing with a cloud of . particles, each of mass ., the phase space would be 2.-dimensional with coordinates .., ..,..., .., .., .., ..., ... Note that . indicates the number of independent positions oheterogeneous 发表于 2025-3-27 19:47:02
Maren Zschachonal with coordinates . and . or . and ., as in the common Newtonian notation. If instead we were dealing with a cloud of . particles, each of mass ., the phase space would be 2.-dimensional with coordinates .., ..,..., .., .., .., ..., ... Note that . indicates the number of independent positions oexcursion 发表于 2025-3-28 00:13:47
http://reply.papertrans.cn/47/4611/461027/461027_37.png清真寺 发表于 2025-3-28 03:58:25
Maren Zschachroximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While 978-3-642-59281-2Series ISSN 1431-9381MERIT 发表于 2025-3-28 09:31:28
http://reply.papertrans.cn/47/4611/461027/461027_39.pngCLEFT 发表于 2025-3-28 13:47:49
Maren Zschachntionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.978-3-030-44307-8978-3-030-44305-4Series ISSN 1860-0832 Series E-ISSN 1860-0840