Symbolic dynamics for pointwise hyperbolic systems on open regions
Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism $f:M\rightarrow M$ on an open invariant subset $O\subset M$ , which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2025-02, Vol.45 (2), p.595-648 |
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| container_title | Ergodic theory and dynamical systems |
| container_volume | 45 |
| creator | WU, CHUPENG ZHOU, YUNHUA |
| description | Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism
$f:M\rightarrow M$
on an open invariant subset
$O\subset M$
, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f. |
| doi_str_mv | 10.1017/etds.2024.47 |
| format | Article |
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$f:M\rightarrow M$
on an open invariant subset
$O\subset M$
, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.</description><identifier>ISSN: 0143-3857</identifier><identifier>EISSN: 1469-4417</identifier><identifier>DOI: 10.1017/etds.2024.47</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Estimates ; Euclidean space ; Hyperbolic systems ; Invariants ; Isomorphism ; Liapunov exponents ; Orbits ; Original Article</subject><ispartof>Ergodic theory and dynamical systems, 2025-02, Vol.45 (2), p.595-648</ispartof><rights>The Author(s), 2024. Published by Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c189t-d08eef6e44a52999eb5cf89f8c53b2c70f989610e6824593f5c5b6b01af517f33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0143385724000476/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,776,780,27901,27902,55603</link.rule.ids></links><search><creatorcontrib>WU, CHUPENG</creatorcontrib><creatorcontrib>ZHOU, YUNHUA</creatorcontrib><title>Symbolic dynamics for pointwise hyperbolic systems on open regions</title><title>Ergodic theory and dynamical systems</title><addtitle>Ergod. Th. Dynam. Sys</addtitle><description>Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism
$f:M\rightarrow M$
on an open invariant subset
$O\subset M$
, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.</description><subject>Estimates</subject><subject>Euclidean space</subject><subject>Hyperbolic systems</subject><subject>Invariants</subject><subject>Isomorphism</subject><subject>Liapunov exponents</subject><subject>Orbits</subject><subject>Original Article</subject><issn>0143-3857</issn><issn>1469-4417</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNptkEtLAzEYRYMoWKs7f0DArTPmOUmWWnxBwYW6DjOZLzWlMxmTKTL_3pYW3Li6m3PvhYPQNSUlJVTdwdjmkhEmSqFO0IyKyhRCUHWKZoQKXnAt1Tm6yHlNCOFUyRl6eJ-6Jm6Cw-3U111wGfuY8BBDP_6EDPhrGiAdiDzlEbqMY4_jAD1OsAqxz5fozNebDFfHnKPPp8ePxUuxfHt-XdwvC0e1GYuWaABfgRC1ZMYYaKTz2njtJG-YU8QbbSpKoNJMSMO9dLKpGkJrL6nynM_RzWF3SPF7C3m067hN_e7SciqZUJRpvaNuD5RLMecE3g4pdHWaLCV2b8nuLdm9JSvUDi-PeN01KbQr-Fv9t_ALeoxqlA</recordid><startdate>202502</startdate><enddate>202502</enddate><creator>WU, CHUPENG</creator><creator>ZHOU, YUNHUA</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>202502</creationdate><title>Symbolic dynamics for pointwise hyperbolic systems on open regions</title><author>WU, CHUPENG ; ZHOU, YUNHUA</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c189t-d08eef6e44a52999eb5cf89f8c53b2c70f989610e6824593f5c5b6b01af517f33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Estimates</topic><topic>Euclidean space</topic><topic>Hyperbolic systems</topic><topic>Invariants</topic><topic>Isomorphism</topic><topic>Liapunov exponents</topic><topic>Orbits</topic><topic>Original Article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>WU, CHUPENG</creatorcontrib><creatorcontrib>ZHOU, YUNHUA</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Ergodic theory and dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>WU, CHUPENG</au><au>ZHOU, YUNHUA</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symbolic dynamics for pointwise hyperbolic systems on open regions</atitle><jtitle>Ergodic theory and dynamical systems</jtitle><addtitle>Ergod. Th. Dynam. Sys</addtitle><date>2025-02</date><risdate>2025</risdate><volume>45</volume><issue>2</issue><spage>595</spage><epage>648</epage><pages>595-648</pages><issn>0143-3857</issn><eissn>1469-4417</eissn><abstract>Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism
$f:M\rightarrow M$
on an open invariant subset
$O\subset M$
, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/etds.2024.47</doi><tpages>54</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0143-3857 |
| ispartof | Ergodic theory and dynamical systems, 2025-02, Vol.45 (2), p.595-648 |
| issn | 0143-3857 1469-4417 |
| language | eng |
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| source | Cambridge University Press Journals Complete |
| subjects | Estimates Euclidean space Hyperbolic systems Invariants Isomorphism Liapunov exponents Orbits Original Article |
| title | Symbolic dynamics for pointwise hyperbolic systems on open regions |
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